Smoothers & Best-Fit Lines

# Smoothers & Best-Fit Lines
### Derek Ogle, May 2020

---

# Today's Goal

<font size="7">Highlight trends in data with "smoothers" and models (e.g., lines) of best-fit.</font>

---

# Problem to be Addressed

- You want to draw attention to the overall trend and away from the detail.

&nbsp;

--
- May be accomplished by adding a "smoother" to the graph.

--
  - **Parametric** ... regression models (lines, polynomials, nonlinear).

--
  - **Non-parameteric** ... LO(W)ESS or GAM smoothers.
    
---

# Linear Regression

- The line that "best fits" a scatterplot of data.

--
- The line out of all possible lines that is "closest" to the data.

--
  - "Closeness" measured by *residuals* (vertical distances b/w points and line).

--
  - "Best-fit line" has smallest sum of squared residuals.

---

# LO(W)ESS Smoother

- *LO*cally *WE*ighted *S*catterplot *S*moother.

--
- Details are bit involved (you saw this in the preparation video).

--
  - Essentially fits several regressions to "windows" of data.
  - "Stitches" those together to form a "curve."

--
  - `span=` controls size of windows and, thus, smoothing.

---

# Adding Smoothers

- A "smoother" is added with `geom_smooth()`.

&nbsp;

--
- Type of smoother is chosen with `method=`.

--
  - `method="lm"` ... for a linear regression model.
  - `method="loess"` ... for a loess smoother model (default if n<1000).
  - `method="gam"` ... for a GAM smoother (default if n>1000).

&nbsp;

--
- Specifics of models can be controlled with `se`, `formula=`, `n=`, `span=`.
  - `se=TRUE` ... adds a 95% confidence band (*default*).

--
  - Others are beyond the scope of this class (though we will look at a couple).

---

### Linear Regression

---

# Background

- Examine the relationship between the total volume of avocados sold and the average price of an avocado, for *only* organic avocados.

--
- Loaded the data into the `avoc` object.

```r
## #!# Set to your own working directory and have just your filename below.
avoc <- read.csv("https://raw.githubusercontent.com/droglenc/NCData/master/Avocados.csv",
                stringsAsFactors=FALSE,quote="") %>%
  filter(region=="GreatLakes",type=="organic") %>%
  mutate(type=factor(type),year=factor(year)) %>%
  select(year,region,Total.Volume,AveragePrice)
head(avoc)
```

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
4 2015 GreatLakes     71502.74         1.60
5 2015 GreatLakes     59169.17         1.61
6 2015 GreatLakes     67773.07         1.57
```

---

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice)) +  
  geom_point(size=1.25,pch=21,color="black",fill="gray70") +  
  scale_x_continuous(  
    name="Average Price",  
  ) +  
  scale_y_continuous(  
    breaks=seq(50000,350000,50000),  
  ) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_scat_non_seq_1_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice)) +  
  geom_point(size=1.25,pch=21,color="black",fill="gray70") +  
  scale_x_continuous(  
    name="Average Price",  
*   labels=scales::dollar
  ) +  
  scale_y_continuous(  
    breaks=seq(50000,350000,50000),  
  ) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_scat_non_seq_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice)) +  
  geom_point(size=1.25,pch=21,color="black",fill="gray70") +  
  scale_x_continuous(  
    name="Average Price",  
    labels=scales::dollar  
  ) +  
  scale_y_continuous(  
    breaks=seq(50000,350000,50000),  
*   labels=scales::unit_format(unit="",scale=1/1000),
  ) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_scat_non_seq_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice)) +  
  geom_point(size=1.25,pch=21,color="black",fill="gray70") +  
  scale_x_continuous(  
    name="Average Price",  
    labels=scales::dollar  
  ) +  
  scale_y_continuous(  
    breaks=seq(50000,350000,50000),  
    labels=scales::unit_format(unit="",scale=1/1000),  
*   name="Thousands of Bags Sold"
  ) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_scat_non_seq_4_output-1.png" width="100%" />
]]

---

### Adding a Regression Line

---

```r
p +  
  geom_smooth(  
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm1_non_seq_1_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p +  
  geom_smooth(  
*   method="lm",
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm1_non_seq_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p +  
  geom_smooth(  
    method="lm",  
*   color="red",
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm1_non_seq_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p +  
  geom_smooth(  
    method="lm",  
    color="red",  
*   fill="red",
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm1_non_seq_4_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p +  
  geom_smooth(  
    method="lm",  
    color="red",  
    fill="red",  
*   se=FALSE
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm1_non_seq_5_output-1.png" width="100%" />
]]

---

### Adding a Regression Line by Group

---

# Create and Show a Palette

```r
cbPalette <- c("#999999","#E69F00","#56B4E9","#009E73","#F0E442","#0072B2","#D55E00","#CC79A7")
```

```r
scales::show_col(cbPalette)
```

---

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice,  
                                  )) +  
  geom_point(size=1.25,pch=21) +  
  scale_x_continuous(name="Average Price",labels=scales::dollar) +  
  scale_y_continuous(name="Thousands of Bags Sold",  
                     limits=c(50000,NA),breaks=seq(50000,350000,50000),  
                     labels=scales::unit_format(unit="",scale=1/1000)) +  
  geom_smooth(method="lm") +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm2_non_seq_1_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice,  
*                                 color=year,fill=year
                                  )) +  
  geom_point(size=1.25,pch=21) +  
  scale_x_continuous(name="Average Price",labels=scales::dollar) +  
  scale_y_continuous(name="Thousands of Bags Sold",  
                     limits=c(50000,NA),breaks=seq(50000,350000,50000),  
                     labels=scales::unit_format(unit="",scale=1/1000)) +  
  geom_smooth(method="lm") +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm2_non_seq_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice,  
                                  color=year,fill=year  
                                  )) +  
  geom_point(size=1.25,pch=21) +  
  scale_x_continuous(name="Average Price",labels=scales::dollar) +  
  scale_y_continuous(name="Thousands of Bags Sold",  
                     limits=c(50000,NA),breaks=seq(50000,350000,50000),  
                     labels=scales::unit_format(unit="",scale=1/1000)) +  
  geom_smooth(method="lm") +  
* scale_color_manual(name="Year",values=cbPalette) +
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm2_non_seq_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
p <- ggplot(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice,  
                                  color=year,fill=year  
                                  )) +  
  geom_point(size=1.25,pch=21) +  
  scale_x_continuous(name="Average Price",labels=scales::dollar) +  
  scale_y_continuous(name="Thousands of Bags Sold",  
                     limits=c(50000,NA),breaks=seq(50000,350000,50000),  
                     labels=scales::unit_format(unit="",scale=1/1000)) +  
  geom_smooth(method="lm") +  
  scale_color_manual(name="Year",values=cbPalette) +  
* scale_fill_manual(name="Year",values=cbPalette) +
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
p
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/avoc_lm2_non_seq_4_output-1.png" width="100%" />
]]

---

### Loess Smoother

---

# Background

- Examine the trend in Moose (*Alces alces*) aboundance on Isle Royale over time.

--
- Loaded the data into the `irwm` object.

```r
## #!# Set to your own working directory and have just your filename below.
irmw <- read.csv("https://raw.githubusercontent.com/droglenc/NCData/master/WolvesMoose_IsleRoyale_June2019.csv",
                 na.strings=c("NA","N/A")) %>%
  select(year,wolves,moose,Jan.Feb..temp..F.,ice.bridges..0.none..1...present.) %>%
  rename(winter_temp=Jan.Feb..temp..F.,
         ice_bridges=ice.bridges..0.none..1...present.) %>%
  mutate(ice_bridges=plyr::mapvalues(ice_bridges,from=c(0,1),to=c("no","yes")),
         ice_bridges=factor(ice_bridges))
head(irmw)
```

```
  year wolves moose winter_temp ice_bridges
1 1959     20   538        1.40          no
2 1960     22   564        8.45          no
3 1961     22   572        9.75         yes
4 1962     23   579        2.15         yes
5 1963     20   596       -0.35         yes
6 1964     26   620       12.40          no
```

---

```r
mw <- ggplot(data=irmw,mapping=aes(y=moose,x=wolves)) +  
  geom_point(size=1.25,pch=21,color="black",fill="gray50") +  
  scale_x_continuous(name="Number of Wolves") +  
  scale_y_continuous(name="Number of Moose") +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
mw
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_scat_1_1_output-1.png" width="100%" />
]]

---

### Adding a Loess Line

---

```r
mw +  
  geom_smooth(  
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess1_non_seq_1_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
mw +  
  geom_smooth(  
*   method="loess",
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess1_non_seq_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
mw +  
  geom_smooth(  
    method="loess",  
*   color="darkorange",
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess1_non_seq_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
mw +  
  geom_smooth(  
    method="loess",  
    color="darkorange",  
*   fill="orange",
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess1_non_seq_4_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
mw +  
  geom_smooth(  
    method="loess",  
    color="darkorange",  
    fill="orange",  
*   span=0.6
  )  
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess1_non_seq_5_output-1.png" width="100%" />
]]

---

```r
mw2 <- ggplot(data=irmw,mapping=aes(y=moose,x=wolves,  
                                   )) +  
  geom_point(size=1.25,pch=21) +  
  scale_x_continuous(name="Number of Wolves") +  
  scale_y_continuous(name="Number of Moose",limits=c(0,NA)) +  
  scale_color_manual(name="Ice Bridge?",values=cbPalette) +  
  scale_fill_manual(name="Ice Bridge?",values=cbPalette) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
mw2
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess2_non_seq_1_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
mw2 <- ggplot(data=irmw,mapping=aes(y=moose,x=wolves,  
                                   )) +  
  geom_point(size=1.25,pch=21) +  
  geom_smooth(method="loess",span=0.6) +  
* scale_x_continuous(name="Number of Wolves") +
  scale_y_continuous(name="Number of Moose",limits=c(0,NA)) +  
  scale_color_manual(name="Ice Bridge?",values=cbPalette) +  
  scale_fill_manual(name="Ice Bridge?",values=cbPalette) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
mw2
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess2_non_seq_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
mw2 <- ggplot(data=irmw,mapping=aes(y=moose,x=wolves,  
*                                  color=ice_bridges,fill=ice_bridges
                                   )) +  
  geom_point(size=1.25,pch=21) +  
  geom_smooth(method="loess",span=0.6) +  
  scale_x_continuous(name="Number of Wolves") +  
  scale_y_continuous(name="Number of Moose",limits=c(0,NA)) +  
  scale_color_manual(name="Ice Bridge?",values=cbPalette) +  
  scale_fill_manual(name="Ice Bridge?",values=cbPalette) +  
  theme_bw() +  
  theme(panel.grid.minor=element_blank())  
 
mw2
```
]]
.column[.content[
<img src="Lecture_Smoothers_files/figure-html/moose_loess2_non_seq_3_output-1.png" width="100%" />
]]

---

### User-Defined Models

---

# User-Defined Models

- Linear regression and LOESS smoothers are effective for highlighting trends.

--
- However, you may also want to show the fit of other models.

--
  - An effective way to do this is to fit the model, predict values of Y for given values of X, and then overlay a line that connects the X and predicted Y points.

--
  - This is flexible but requires keeping track of two data sets.

--
  - Will demonstrate with a linear model and then a logistic regression model.

---

# Showing Linear Regression II

- Return to predicting bags of organic avocados sold from price of an avocado.

--
- Fit the linear model

```r
lmavoc <- lm(Total.Volume~AveragePrice,data=avoc)
lmavoc
```

```

Call:
lm(formula = Total.Volume ~ AveragePrice, data = avoc)

Coefficients:
 (Intercept)  AveragePrice  
      314773       -123162  
```

---

# Showing Linear Regression II

- Create many **ordered** values of X across range of X.

```r
x <- seq(0.75,1.90,0.01)
```

--
- Predict values of Y for each X.

```r
y <- predict(lmavoc,data.frame(AveragePrice=x),interval="confidence")
```

--
- Put together as a data.frame.

```r
preds <- data.frame(x,y)
head(preds)
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
4 0.78 218706.1 189955.9 247456.3
5 0.79 217474.5 189099.5 245849.5
6 0.80 216242.9 188242.7 244243.1
```

---

# Showing Linear Regression II

- Plot the points, but make sure `data=` and `mapping=` for the **raw data** are in `geom_point()`.

--
- Plot line, but make sure `data=` and `mapping=` for the **predicted** results are in `geom_line()`.

---

```r
*head(avoc,n=3)
*head(preds,n=3)
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

*ggplot() +
* geom_point(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice),
*            size=1.25,pch=21,color="black",fill="gray70")
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc3_user_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

ggplot() +  
  geom_point(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice),  
             size=1.25,pch=21,color="black",fill="gray70") +  
* geom_line(data=preds,mapping=aes(y=fit,x=x),
*           size=1,color="blue")
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc3_user_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

ggplot() +  
  geom_point(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice),  
             size=1.25,pch=21,color="black",fill="gray70") +  
  geom_line(data=preds,mapping=aes(y=fit,x=x),  
            size=1,color="blue") +  
* scale_x_continuous(name="Average Price",labels=scales::dollar) +
* scale_y_continuous(name="Thousands of Bags Sold",
*                    breaks=seq(50000,350000,50000),
*                    labels=scales::unit_format(unit="",scale=1/1000)) +
* theme_bw() +
* theme(panel.grid.minor=element_blank())
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc3_user_4_output-1.png" width="100%" />
]]

---

### Showing the Confidence Band

---

```r
*head(avoc,n=3)
*head(preds,n=3)
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

*ggplot() +
* geom_ribbon(data=preds,mapping=aes(x=x,ymin=lwr,ymax=upr),
*             fill="blue",alpha=0.25)
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc4_user_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

ggplot() +  
  geom_ribbon(data=preds,mapping=aes(x=x,ymin=lwr,ymax=upr),  
              fill="blue",alpha=0.25) +  
* geom_point(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice),
*            size=1.25,pch=21,color="black",fill="gray70")
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc4_user_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc4_user_4_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(avoc,n=3)  
head(preds,n=3)

ggplot() +  
  geom_ribbon(data=preds,mapping=aes(x=x,ymin=lwr,ymax=upr),  
              fill="blue",alpha=0.25) +  
  geom_point(data=avoc,mapping=aes(y=Total.Volume,x=AveragePrice),  
             size=1.25,pch=21,color="black",fill="gray70") +  
  geom_line(data=preds,mapping=aes(y=fit,x=x),  
            size=1,color="blue") +  
* scale_x_continuous(name="Average Price",labels=scales::dollar) +
* scale_y_continuous(name="Thousands of Bags Sold",
*                    breaks=seq(50000,350000,50000),
*                    labels=scales::unit_format(unit="",scale=1/1000)) +
* theme_bw() +
* theme(panel.grid.minor=element_blank())
```
]]
.column[.content[

```
  year     region Total.Volume AveragePrice
1 2015 GreatLakes     66775.85         1.49
2 2015 GreatLakes     62669.16         1.55
3 2015 GreatLakes     65341.66         1.53
```

```
     x      fit      lwr      upr
1 0.75 222401.0 192523.2 252278.8
2 0.76 221169.4 191667.8 250671.0
3 0.77 219937.7 190812.0 249063.5
```

<img src="Lecture_Smoothers_files/figure-html/avoc4_user_5_output-1.png" width="100%" />
]]

---

### User-Defined Models (Another Example)

---

```r
bm <- read.csv("https://raw.githubusercontent.com/droglenc/NCData/master/Batmorph.csv")

logreg <- glm(subsp~canine,data=bm,family="binomial")
logreg
```

```

Call:  glm(formula = subsp ~ canine, family = "binomial", data = bm)

Coefficients:
(Intercept)       canine  
      35.52      -111.12

Degrees of Freedom: 117 Total (i.e. Null);  116 Residual
Null Deviance:	    163 
Residual Deviance: 97.18 	AIC: 101.2
```

```r
x <- seq(0.250,0.375,length.out=200)
y <- predict(logreg,data.frame(canine=x),type="response",se=TRUE)
preds <- data.frame(x,y)
head(preds)
```

```
          x       fit       se.fit residual.scale
1 0.2500000 0.9995633 0.0006258162              1
2 0.2506281 0.9995318 0.0006652159              1
3 0.2512563 0.9994980 0.0007070408              1
4 0.2518844 0.9994617 0.0007514356              1
5 0.2525126 0.9994228 0.0007985531              1
6 0.2531407 0.9993811 0.0008485547              1
```

---

```r
*head(bm,n=3)
*head(preds,n=3)
```
]]
.column[.content[

```
    subsp bodymass skulllength canine coronoid wingspan hab
1 semotus    19.50       1.597  0.326    0.303    0.358   A
2 semotus    16.22       1.552  0.308    0.282    0.358   A
3 semotus    16.98       1.563  0.291    0.292    0.359   A
```

```
          x       fit       se.fit residual.scale
1 0.2500000 0.9995633 0.0006258162              1
2 0.2506281 0.9995318 0.0006652159              1
3 0.2512563 0.9994980 0.0007070408              1
```
]]
---
class: split-50
count: false

```r
head(bm,n=3)  
head(preds,n=3)

*ggplot() +
* geom_ribbon(data=preds,mapping=aes(x=x,
*                                    ymin=fit-2*se.fit,
*                                    ymax=fit+2*se.fit),
*             fill="blue",alpha=0.25)
```
]]
.column[.content[

```
          x       fit       se.fit residual.scale
1 0.2500000 0.9995633 0.0006258162              1
2 0.2506281 0.9995318 0.0006652159              1
3 0.2512563 0.9994980 0.0007070408              1
```

<img src="Lecture_Smoothers_files/figure-html/logistic2_user_2_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(bm,n=3)  
head(preds,n=3)

ggplot() +  
  geom_ribbon(data=preds,mapping=aes(x=x,  
                                     ymin=fit-2*se.fit,  
                                     ymax=fit+2*se.fit),  
              fill="blue",alpha=0.25) +  
* geom_line(data=preds,mapping=aes(x=x,y=fit),color="blue",size=1)
```
]]
.column[.content[

<img src="Lecture_Smoothers_files/figure-html/logistic2_user_3_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(bm,n=3)  
head(preds,n=3)

<img src="Lecture_Smoothers_files/figure-html/logistic2_user_4_output-1.png" width="100%" />
]]
---
class: split-50
count: false

```r
head(bm,n=3)  
head(preds,n=3)

ggplot() +  
  geom_ribbon(data=preds,mapping=aes(x=x,  
                                     ymin=fit-2*se.fit,  
                                     ymax=fit+2*se.fit),  
              fill="blue",alpha=0.25) +  
  geom_line(data=preds,mapping=aes(x=x,y=fit),color="blue",size=1) +  
  geom_point(data=bm,mapping=aes(x=canine,y=as.numeric(subsp)-1),  
             size=1.5,alpha=0.25) +  
* scale_x_continuous(name="Canine Tooth Height (cm)",
*                    expand=expansion(mult=0)) +
* scale_y_continuous(name="Probability of Semotus",
*                    expand=expansion(mult=0.01)) +
* theme_bw() +
* theme(panel.grid.minor=element_blank())
```
]]
.column[.content[

<img src="Lecture_Smoothers_files/figure-html/logistic2_user_5_output-1.png" width="100%" />
]]

---

# Next Time

<font size="7">We will discuss how to add titles, labels, and annotations to your graphs.</font>