MLR Example

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# MLR Example
### STAT 021 with Prof Suzy
### Swarthmore College

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## MLR with only numerical predictor variables 
### Public school SAT data

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```r
SAT_data <- read_table2("Data/sat_data.txt", col_names=FALSE, cols(col_character(), col_double(), col_double(), col_double(), col_double(), col_double(), col_double(), col_double()))
colnames(SAT_data) = c("State", "PerPupilSpending", "StuTeachRatio", "Salary", "PropnStu", "SAT_verbal", "SAT_math", "SAT_tot")
SAT_data <- SAT_data %>% mutate(prop_taking_SAT = PropnStu/100) %>% select(-PropnStu)

head(SAT_data)  ##note: please dont print out entire data sets in your HW solutions!
```

```
## # A tibble: 6 x 8
##   State      PerPupilSpending StuTeachRatio Salary SAT_verbal SAT_math SAT_tot
##   <chr>                 <dbl>         <dbl>  <dbl>      <dbl>    <dbl>   <dbl>
## 1 Alabama                4.40          17.2   31.1        491      538    1029
## 2 Alaska                 8.96          17.6   48.0        445      489     934
## 3 Arizona                4.78          19.3   32.2        448      496     944
## 4 Arkansas               4.46          17.1   28.9        482      523    1005
## 5 California             4.99          24     41.1        417      485     902
## 6 Colorado               5.44          18.4   34.6        462      518     980
## # … with 1 more variable: prop_taking_SAT <dbl>
```

```r
names(SAT_data)
```

```
## [1] "State"            "PerPupilSpending" "StuTeachRatio"    "Salary"          
## [5] "SAT_verbal"       "SAT_math"         "SAT_tot"          "prop_taking_SAT"
```
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## Public school SAT data
### What are the factors affecting SAT scores?

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## Public school SAT data
### First: Visualize 2D plots for every pair of predictors

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```r
SAT_data %>% select(-State) %>% pairs(pch=16) 
```

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## Public school SAT data
### First: Visualize 2D plots for every pair of predictors

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```r
SAT_data %>% select(-c(State, SAT_verbal, SAT_math)) %>% pairs(pch=16) 
```

<img src="Figs/class15_scatter2-1.png" style="display: block; margin: auto;" />
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## Public school SAT data
### Second: Fit a linear regression model and plot the residuals

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```r
MLR_SAT <- lm(SAT_tot ~ PerPupilSpending + StuTeachRatio, data = SAT_data)
summary(MLR_SAT)
```

```
## 
## Call:
## lm(formula = SAT_tot ~ PerPupilSpending + StuTeachRatio, data = SAT_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -147.694  -51.816    6.258   37.756  127.742 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      1136.336    107.803  10.541 5.69e-14 ***
## PerPupilSpending  -22.308      7.956  -2.804  0.00731 ** 
## StuTeachRatio      -2.295      4.784  -0.480  0.63370    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 70.48 on 47 degrees of freedom
## Multiple R-squared:  0.149,	Adjusted R-squared:  0.1128 
## F-statistic: 4.114 on 2 and 47 DF,  p-value: 0.02258
```
]

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## Public school SAT data
### Second: Fit a linear regression model and plot the residuals

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<img src="Figs/class15_3dplot2-1.png" height="400" style="display: block; margin: auto;" />
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## Public school SAT data
### Second: Fit a linear regression model and plot the residuals

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<img src="Figs/class15_resid-1.png" height="400" style="display: block; margin: auto;" />
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## Public school SAT data
### Second: Fit a linear regression model and plot the residuals

```r
SAT_resid_data <- SAT_data %>% 
                  mutate(residuals = MLR_SAT$residuals,
                         fitted_vals = MLR_SAT$fitted.values) 
ggplot(SAT_resid_data) +
  geom_point(aes(x=fitted_vals, y=residuals)) + 
  labs(title="Residual plot", subtitle="Public school SAT scores",
       x="Predicted SAT Scores", y="Residuals") + 
  geom_hline(yintercept=0) + ylim(-200,200)
```