Chapter 12.1, Problem 7E

(a)

To determine

To find: the estimate for ${\beta }_0$ , explain this value.

Answer to Problem 7E

  $b_0$ =-0.012701

The content of blood alcohol is on average -0.012701, when the student drinks 0 beers.

Explanation of Solution

Given:

  

  ${\beta }_0$ Corresponds to the y intercepting to the population regression line, it can be estimated by the y intercept $b_0$ of the regression line of sample.

  $b_0$ =-0.012701

The y-intercept shows the average value of y when x=0

The content of blood alcohol is on average -0.012701, when the student drinks 0 beers.

(b)

To determine

To find: the estimate for ${\beta }_1$ , explain this value.

Answer to Problem 7E

The beer alcohol content increases by 0.017964 per beer on average.

Explanation of Solution

Given:

  

  ${\beta }_1$ Corresponds to the slope of the population regression line, it can be estimated by the slope of the $b_1$ of the regression line of sample.

  $b_1$ = 0.017964

Slope is representing the average increase of y per unit of x.

The beer alcohol content increases by 0.017964 per beer on average.

(c)

To determine

To find: the estimate for $\sigma$ , explain this value.

Answer to Problem 7E

The expected BAC of an individual that is at least 21 years of age deviates on average by 0.0204 about the actual BAC.

Explanation of Solution

Given:

  

  $\sigma$ Shows the population standard deviation of the residual, it is estimated by the sample standard deviation of the residuals s.

s=0.0204

Standard error of the estimate s shows the average error of prediction, therefore the average deviation between actual values of y and the predicted y values.

The expected BAC of an individual that is at least 21 years of age deviates on average by 0.0204 about the actual BAC.

(d)

To determine

To find: the standard error of the slope $S{E}_{b_1}$ , explain this value.

Answer to Problem 7E

Slope of regression line vary on average about 0.0024 from the slope of the population regression line.

Explanation of Solution

Given:

  

Standard error of the slope $S{E}_{b_1}$ is mention in the row of “Beers” and in the column s. E. Of coeff of the mention computer output

  $S{E}_{b_1}$ =0.0024

Standard error of the slope shows the average deviation of the slope of regression line of the sample from the population regression line of the slope.

Slope of regression line vary on average about 0.0024 from the slope of the population regression line.