# Practice 15 How to Conduct Linear Regression in R

## 15.1 Directions

In this practice exercise, you will estimate a linear regression in R.

## 15.2 A closer look at the code

A random sample of 11 statistics students produced the following data, where x is the third exam score out of 80, and y is the final exam score out of 200. Can you predict the final exam score of a random student if you know the third exam score?

x (third exam score) y (final exam score)
65 175
67 133
71 185
71 163
66 126
75 198
67 153
70 163
71 159
69 151
69 159

### 15.2.1 Scatterplot

exam.third <- c(65, 67, 71, 71, 66, 75, 67, 70, 71, 69, 69)
exam.final <- c(175, 133, 185, 163, 126, 198, 153, 163, 159, 151, 159)

plot(y=exam.final,x=exam.third)

### 15.2.2 Summary statistics

There appears to be a linear relationship between the two variables: price and income. But we also want to consider the summary statistics.

quantile(exam.final)
##   0%  25%  50%  75% 100%
##  126  152  159  169  198
quantile(exam.third)
##   0%  25%  50%  75% 100%
##   65   67   69   71   75

### 15.2.3 Estimate linear regression

In r, the lm() command is used to estimate linear regression models. The “lm” stands for linear model.

exam.lm <- lm(exam.final ~ exam.third)
summary(exam.lm)
##
## Call:
## lm(formula = exam.final ~ exam.third)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -19.095  -9.404  -1.404   6.268  34.733
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -173.513    125.765  -1.380   0.2010
## exam.third     4.827      1.816   2.658   0.0262 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.41 on 9 degrees of freedom
## Multiple R-squared:  0.4397, Adjusted R-squared:  0.3774
## F-statistic: 7.063 on 1 and 9 DF,  p-value: 0.02615

### 15.2.4 Scatterplot With Regression Line

plot(y=exam.final,x=exam.third)
abline(exam.lm)

### 15.2.5 Residual Diagnostics

exam.lm.res = resid(exam.lm)

plot(x=exam.third,y=exam.lm.res)
abline(h=0)

## 15.3 Now you try

Use R to complete the following activities (this is just for practice you do not need to turn anything in).

Use the mtcars data set to plot mpg vs hp.