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Chapter 12: Q. 8 (page 789)

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

a. What is the estimate for β0? Interpret this value.

b. What is the estimate for β1? Interpret this value.

c. What is the estimate for σ? Interpret this value.

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

Short Answer

Expert verified

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 0.008569per beer.

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

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

Step by step solution

01

Part (a) Step 1 : Given information

We have to find the estimate for β0, explain this value.

02

Part (a) Step 2 : Simplification

b0Corresponding0to 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.
03

Part (b) Step 1 : Given information

We have to find the estimate for β1, explain this value.

04

Part (b) Step 2 : Simplification

The slope of the population regression line can be determined using the slope of the b1of 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 by0.008569 per beer.
05

Part (c) Step 1 : Given information

We have to find the estimate for σ, explain this value.

06

Part (c) Step 2 : Simplification

The sample standard deviation of the residuals sis used to determine the population standard deviation of the residual.
s=0.1886
The standard error of the estimate srepresents 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 0.1886on average.
07

Part (d) Step 1 : Given information

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

08

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 0.002456on average.

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Most popular questions from this chapter

Less mess? Kerry and Danielle wanted to investigate if tapping on a can of soda would reduce the amount of soda expelled after the can has been shaken. For their experiment, they vigorously shook 40cans of soda and randomly assigned each can to be tapped for 0seconds, 4seconds, 8seconds, or 12seconds. After opening the cans and waiting for the fizzing to stop, they measured the amount expelled (in milliliters) by subtracting the amount remaining from the original amount in the can. Here are their data:

Here is some computer output from a least-squares regression analysis of these data. Construct and interpret a 95%confidence interval for the slope of the true regression line.

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Assuming that the conditions for inference are met, which of the following significance tests should be used to determine whether the adjusters’ suspicion is correct?

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Which of the following is the equation of the least-squares regression line for predicting height from foot length?

a. height^=10.2204+0.4117(foot length) height^=10.2204+0.4117(foot length)

b.height^=0.4117+3.0867 (foot length) height^=0.4117+3.0867(foot length)

c. height^=91.9766+3.0867(foot length) height^=91.9766+3.0867(foot length)

d. height^=91.9766+6.47044 (foot length)height^=91.9766+6.47044(foot length)

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The students in Mr. Shenk’s class measured the arm spans and heights (in inches) of a random sample of 18students from their large high school. Here is computer output from a least-squares regression analysis of these data. Construct and interpret a 90%confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

PredictorCoefStdevt-ratioPConstant11.5475.6002.060.056Armspan0.840420.0809110.390.000S=1.613R-Sq=87.1%R-Sq(adj)=86.3%

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightwere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is a 95%confidence interval for the population slope β1?

a.3.0867±0.4117

b. 3.0867±0.8518

c.3.0867±0.8069

d.3.0867±0.8497

e.localid="1654193042763" 3.0867±0.8481
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