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Chapter 12: Q. 7 (page 788)

Beer and BAC Refer to Exercise 5. Here is computer output from the least-squares regression analysis of the beer and blood alcohol data.

a. What is the estimate for 尾0? Interpret this value.

b. What is the estimate for 尾1? Interpret this value.

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

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

Short Answer

Expert verified

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

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

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

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

Step by step solution

01

Part (a) Step 1 : Given information

We have to find the estimate for 尾0, explain this value.

02

Part (a) Step 2 : Simplification

尾0corresponds to the y intercepting to the population regression line, it can be estimated by the y intercept b0of the regression line of sample.

b0=-0.012701

When x=0, the y-intercept shows the average value of y.
When a student drinks 0beers, his blood alcohol level is on average -0.012701.
03

Part (b) Step 1 : Given information

We have to findthe estimate for 尾1, 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=0.017964

The average rise in yper unit of xis represented by slope.
On average, the alcohol concentration of beer rises by 0.017964every beer.
05

Part (c) Step 1 : Given information

We have to find the estimate for 蟽, 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=0.0204
The standard error of the estimate s represents the average prediction error, and thus the average deviation between actual and expected y values.
The anticipated BAC of a person who is at least 21years old differs from the actual BAC by 0.0204on 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 "Beers" and the column s.E, the standard error of the slopeSEb1 is mentioned.
The mentioned computer output's coeff
SEb1=0.0024
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 0.0024on average.

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