A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression model yielded the following results. = 24 = 124 = 42 = 338 = 196 Calculate the sample correlation coefficient.
A).7977
B).6364
C).3780
D).1428

Question

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression model yielded the following results.  = 24  = 124  = 42  = 338  = 196 Calculate the sample correlation coefficient.
A).7977 
B).6364 
C).3780 
D).1428

Quizplus · Accepted Answer

We need to use the formula for calculating the sample correlation coefficient:
r = (nΣXY - ΣXΣY) / sqrt[(nΣX^2 - (ΣX)^2)(nΣY^2 - (ΣY)^2)]
where n = 6, ΣX = 736, ΣY = 734, ΣXY = 68515, ΣX^2 = 49320, and ΣY^2 = 64156.
Plugging in these values, we get:
r = (6*68515 - 736*734) / sqrt[(6*49320 - 736^2)(6*64156 - 734^2)]
r = 0.7977
Therefore, the sample correlation coefficient is 0.7977, which corresponds to choice A.

A Local Tire Dealer Wants to Predict the Number of Tires