Continuing on the Boston dataset

Questions

• Answer the questions about the following regression output

> lm.fit <- lm(medv ~ crim, data = Boston)
> summary(lm.fit)

Call:
lm(formula = medv ~ crim, data = Boston)

Residuals:
    Min      1Q  Median      3Q     Max 
-16.957  -5.449  -2.007   2.512  29.800 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 24.03311    0.40914   58.74   <2e-16 ***
crim        -0.41519    0.04389   -9.46   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.484 on 504 degrees of freedom
Multiple R-squared:  0.1508,	Adjusted R-squared:  0.1491 
F-statistic: 89.49 on 1 and 504 DF,  p-value: < 2.2e-16

• MC1:
  A) Crime rate has a significant impact (p < 0.05) on the median value of owner-occupied homes
  B) The \(R^2\) of our model is 0.1508.
  • 1) Both statements are true.
  • 2) Both statements are false.
  • 3) A is true and B is false.
  • 4) A is false and B is true.
• MC2:
  A) We cannot reject the null hypothesis that all coefficient are zero.
  B) There is a negative relationship between the median value of owner-occupied homes and crime rate. The higher crime rate rises, the lower home values will be.
  • 1) Both statements are true.
  • 2) Both statements are false.
  • 3) A is true and B is false.
  • 4) A is false and B is true.