Chapter 12.1, Problem 8E

(a)

To determine

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

Answer to Problem 8E

  $b_0$ =0.12049

The proportion of perch killed is on average 0.12049, when the number of perch in the pen is zero.

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.

  $b_0$ =0.12049

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

The proportion of perch killed is on average 0.12049, when the number of perch in the pen is zero.

(b)

To determine

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

Answer to Problem 8E

The proportion of perch killed increases by 0.008569 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.

  $b_1$ = 0.008569

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

The proportion of perch killed increases by 0.008569 per beer on average.

(c)

To determine

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

Answer to Problem 8E

The expected proportion of perch killed deviates on average by 0.1886 from the actual proportion of perch killed.

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=0.1886

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 proportion of perch killed deviates on average by 0.1886 from the actual proportion of perch killed.

(d)

To determine

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

Answer to Problem 8E

Slope of regression line vary on average about 0.002456 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 “Perch” and in the column “stdev.” of the mention computer output

  $S{E}_{b_1}$ =0.002456

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 0.002456 from the slope of the population regression line.