Question

Prey attracts predators . Here is computer output from the least-squares regression analysis of the perch data

a. What is the estimate for $\beta 0$? Interpret this value.

b. What is the estimate for $\beta 1$? Interpret this value.

c. What is the estimate for $\sigma$? Interpret this value.

d. Give the standard error of the slope $SEb1$. Interpret this value.

Short answer

a. When the number of perch in the pen is zero, the proportion of perch killed is on average $0.12049$.

b. On average, the proportion of perch killed increases by $0.008569$per beer.

c. The projected proportion of perch killed differs from the actual proportion of perch killed by $0.1886$on average.

d. The slope of the regression line differs from the slope of the population regression line by around $0.002456$on average.

Step-by-step solution

Part (a) Step 1 : Given information

We have to find the estimate for $\beta 0$, explain this value.

Part (a) Step 2 : Simplification

$b0$Corresponding$0$to the y intercepting the population regression line, which may be approximated using the sample regression line's y intercept .

$b0=0.12049$

When x=$0$, the y-intercept shows the average value of y.

When the number of perch in the pen is zero, the proportion of perch killed is on average $0.12049.$

Part (b) Step 1 : Given information

We have to find the estimate for $\beta 1$, explain this value.

Part (b) Step 2 : Simplification

The slope of the population regression line can be determined using the slope of the $b1$of the sample regression line.

$b1=0.008569$

The average rise in y per unit of x is represented by slope.

On average, the proportion of perch killed increases by$0.008569$ per beer.

Part (c) Step 1 : Given information

We have to find the estimate for $\sigma$, explain this value.

Part (c) Step 2 : Simplification

The sample standard deviation of the residuals $s$is used to determine the population standard deviation of the residual.

$s=0.1886$

The standard error of the estimate $s$represents the average prediction error, and thus the average deviation between actual and expected y values.

The projected proportion of perch killed differs from the actual proportion of perch killed by $0.1886$on average.

Part (d) Step 1 : Given information

We have to find the standard error of the slope $SEb1$, explain this value.

Part (d) Step 2 : Simplification

In the row "Perch" and the column "stdev." of the mentioned computer output, the standard error of the slope $SEb1$ is mentioned.

$SEb1=0.002456$

The average divergence of the slope of the sample regression line from the population regression line of the slope is shown by the standard error of the slope.

The slope of the regression line differs from the slope of the population regression line by around $0.002456$on average.