Question

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 ${\beta }_0$? 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 $S{E}_{b_1}$. Interpret this value.

Short answer

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

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

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

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

${\beta }_0$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.

$b_0=-0.012701$

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

When a student drinks $0$beers, his blood alcohol level is on average $-0.012701$.

Part (b) Step 1 : Given information

We have to findthe 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 $b_1$of the sample regression line.

$b_1=0.017964$

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

On average, the alcohol concentration of beer rises by $0.017964$every 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.

$s=0.0204$

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 $21$years old differs from the actual BAC by $0.0204$on average.

Part (d) Step 1 : Given information

We have to find the standard error of the slope $S{E}_{b_1}$, explain this value.

Part (d) Step 2 : Simplification

In the row "Beers" and the column $s.E$, the standard error of the slope$S{E}_{b_1}$ is mentioned.

The mentioned computer output's coeff

$S{E}_{b_1}=0.0024$

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 $0.0024$on average.