James is from Georgia and dislikes the cold weather here in Indiana. As a result
ID: 3157751 • Letter: J
Question
James is from Georgia and dislikes the cold weather here in Indiana. As a result, whenever it is cold, James tends to miss more classes. Below is a scatterplot of the data for each of the 11 semesters James attended college in Indiana (4 spring, 4 fall, 3 summer). The temperatures displayed are the average temperature of the semester (in degrees Fahrenheit). Here is the data and its scatterplot. The regression equation and r^2 are displayed on the graph above. Which is the likely explanatory variable? Which is the likely response variable? What is the slope of the regression line? What does it mean in terms of the story? Describe the strength and direction of the relationship between temperature and the number of classes missed. Suppose the average temperature for a semester is 82 degree F. Predict how many classes James will miss. Is this a valid prediction? Calculate the residual for the semester with an average temperature of 57 degree F. What is the correlation coefficient between the number of classes missed and the average semester temperature? Is this correlation strong, weak, or moderate? If the average semester temperature were to increase from 40 degree F to 50 degree F, what is the predicted change in the classes missed? What percent in the variation in the number of classes missed is NOT explained by the linear relationship with the average semester temperature?Explanation / Answer
a) The explanatory variable is temparature. The response variable is classes missed.
b) The slope oof the regression line -0.2405. It means that for every unit increse in the temparature the number of classes missed on the average is decreased by a the factor 0.2405
c) The r2 value is 0.9422 hence the relationship is strong and slope value is negative hence the direction is negative.
d) The predicted value corresponding to 82oF is 0.317 i.e., approximately 0. This prediction valid
e) The residual for 57oF is (7-6.3295)=0.6705
f) The correlation coefficient is r = -0.9707 The correlation is strong and negative
g) The predicted change is 0.2405*(50-40)=2.405
h) The percentage of variation not explained in the number of classes missed is given by 1-r2 =1-0.9422=0.0578. i.e., 5.78%
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