Question

1. at the end of a semester, a math teacher wonders if student attendance has an impact on final exam scores. the teacher selects a random sample of 10 students and records the number of days absent and final exam score for each student. the table shows computer output from a linear regression analysis. a residual plot is also provided. predictor coef se coef t p constant 89.943 4.213 21.347 <0.001 number of absences -2.755 0.896 -3.074 0.015 a. is the linear model appropriate? explain. b. what is the actual exam score for the student with 5 absences? round to the nearest whole point.

Explanation:

Step1: Check linear - model appropriateness

A linear model is appropriate if the residual plot shows a random scatter of points. Looking at the residual plot, the points appear to be randomly scattered around the horizontal axis. There is no obvious pattern (such as a curve, fan - shape, etc.). So, the linear model is appropriate.

Step2: Find the regression equation

The regression equation is of the form $\hat{y}=b_0 + b_1x$, where $b_0$ is the constant coefficient and $b_1$ is the coefficient of the predictor variable. From the table, $b_0 = 89.943$ and $b_1=-2.755$. So the regression equation is $\hat{y}=89.943-2.755x$.

Step3: Predict the score for 5 absences

Substitute $x = 5$ into the regression equation: $\hat{y}=89.943-2.755\times5=89.943 - 13.775=76.168\approx76$. But we are asked for the actual score, and we don't have enough information from the given data to find the actual score. We only have the predicted - score formula and no information about the residuals for the student with 5 absences.

Answer:

a. The linear model is appropriate because the residual plot shows a random scatter of points with no obvious pattern.
b. There is not enough information to determine the actual exam score for the student with 5 absences.