Question

The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 23 male college students by using least squares regression. The following regression equation was obtained from this study:

y = -0.0127+0.0280x

Suppose that the legal limit to drive is a blood alcohol content of 0.08. If Sam consumed 5 beers the model would predict that Sam would be ___ above the legal limit.

Give an exact answer based on the model.

Answer 1

The answer is 0.0473

Answer 2

Answer: 0.0473

Explanation:

To determine how much Sam would be above the legal limit if he consumed 5 beers, we can use the regression equation provided: y = -0.0127 + 0.0280x Here, y represents the blood alcohol content and x represents the number of beers consumed.

Step 1: Substitute x = 5 into the equation. y = -0.0127 + 0.0280(5)

Step 2: Calculate the value of y. y = -0.0127 + 0.14 y = 0.1273 The model predicts that Sam's blood alcohol content would be 0.1273.

Step 3: Calculate the difference from the legal limit. Difference = y - Legal Limit

Difference = 0.1273 - 0.08

Difference = 0.0473

Therefore, the model predicts that if Sam consumed 5 beers, he would be approximately 0.0473 above the legal limit.