The marketing manager of a large supermarket chain has the business objective of
ID: 3154133 • Letter: T
Question
The marketing manager of a large supermarket chain has the business objective of using shelf space efficiently. Toward that goal, she would like to use shelf space to predict the sales of pet food. Using the data set provided, determine if there is a statistically valid linear relationship between the amount of shelf space and the sales of pet food by completing the following tasks.
g) find the value of the coefficient of correlation, r, and state it's meaning;
h) find the value of the coefficient of determination, r2, and state it's meaning;
i) find the values of b0 and b1 and state their meanings;
j) create the single linear regression equation and predict a value for Y when X = 12; and
k) construct a 95% confidence interval estimate of the population slope ?1.
The data given Data Set for Module 5 Group E Store # Sales (S) Shelf Space (feet) 160 220 140 190 240 260 230 270 280 260 290 310 4 10 15 15 20 20 20 10 12Explanation / Answer
g) r = 0.827, it is a measure of the strength and direction of the linear relationship between two variables. 0.827 means there is strong linear relationship detween shelf space and sale
h) R2 = 0.684, It is the proportion of the variance in the dependent variable that is predictable from the independent variable.
i) b0 = 145, it is the intercept of the fitted line
b1 = 7.4, it is the slope of the line, it is the amount by which sales will inclrease if there is a unit increase in shelf size
j) Linear regression equation will be, Y = b0 + b1*X
Y = 145 + 7.4*12 = 233.8
k) 95% CI = (3.86, 10.94)
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