Question

1. a linear regression equation was computed to predict the final - exam score in a statistics class from the score on the first test. the equation was $hat{y}=10 + 0.9x$ where $hat{y}$ is the final - exam score and $x$ is the score on the first test. carla scored 95 on the first test. what is the predicted value of her score on the final exam?

a. 85.5
b. 90
c. 95
d. 95.5
e. none of these

1. a restaurant manager wants to be able to predict the time customers will have to wait for a table based upon how many names are on her waiting list. she collects data on $y =$ the time a group of customers wait for a table, and $x =$ the number of names already on the waiting list when that group is added to the list. she finds that the relationship is roughly linear, and calculates the least - squares regression line. one group waited 15 minutes when there were 4 names ahead of them on the list. which expression below represents the residual for this observation?

a. $4 - 2.8+3.77(15)$
b. $15 - 2.8 + 3.77(4)$
c. $2.8 + 3.77(4)+15$
d. $2.8 + 3.77(4)-15$
e. $2.8 + 3.77(4)-4$

Explanation:

Step1: Substitute x=95 into regression equation

$\hat{y} = 10 + 0.9(95)$

Step2: Calculate the predicted final score

$\hat{y} = 10 + 85.5 = 95.5$

Step3: Recall residual formula: $Residual = y - \hat{y}$

Residual = observed $y$ - predicted $\hat{y}$

Step4: Substitute values into residual formula

Observed $y=15$, $x=4$, regression line $\hat{y}=2.8+3.77x$, so Residual $=15 - [2.8 + 3.77(4)]$

Answer:

1. d. 95.5
2. b. $15 - [2.8 + 3.77(4)]$