Chapter 27, Problem 37E

a)

To determine

To write the equation of the regression line.

Answer to Problem 37E

  $Midterm2=12.0054+0.7210\times Midterm1$

Explanation of Solution

Given:

  

  

  

Using excel,

  

The general regression equation is,

  $\widehat{y}=b_0+b_{1}x$

Here,

  $\begin{array}{l}{b}_0=0.7210\\ b_1=12.0054\end{array}$

Therefore, the equation of regression line is,

  $Midterm2=12.0054+0.7210\times Midterm1$

b)

To determine

To comment on the model.

Explanation of Solution

Given:

  

The equation of regression line is,

  $Midterm2=12.0054+0.7210\times Midterm1$

The scatter plot of the given data shows weak positive linear relationship between Midterm 1 and midterm 2. There seems to be outlying points, but removing them only makes the relationship slightly stronger. There is no obvious pattern in the residual plot. Therefore, the regression model appears to be appropriate. The p-value of the slope is 0.002 which indicates that there is sufficient evidence that the slope is non-zero. The value of R-square is 0.199 indicate that the relationship is weak. Hence, overall relationship between midterm 1 and midterm 2 is weaker.

c)

To determine

To explain whether the model is well predictable from p-value.

Explanation of Solution

Given:

  

The equation of regression line is,

  $Midterm2=12.0054+0.7210\times Midterm1$

The p-value of the slope is 0.002 which indicates that there is sufficient evidence that the slope is non-zero. But the value of R-square is 0.199 indicate that the relationship is weak. Therefore, overall relationship between midterm 1 and midterm 2 is weaker. Hence, it indicates that the prediction of midterm 2 will not accurate.