Regression Analysis The local grocery store wants to predict the daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects the store sales.He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars)and advertising expenditures (in thousands of dollars).The Excel/Mega-Stat output given above summarizes the results of the regression model. Determine a 95% confidence interval estimate of the daily average store sales based on $3000 advertising expenditures? The distance value for this particular prediction is reported as .164.
A)$64,496 to $102.170
B)$33,108 to $133,558
C)$71,324 to $95,342
D)$51,314 to $115,353
E)$42,851 to $83,816

Question

Regression Analysis  The local grocery store wants to predict the daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects the store sales.He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars)and advertising expenditures (in thousands of dollars).The Excel/Mega-Stat output given above summarizes the results of the regression model. Determine a 95% confidence interval estimate of the daily average store sales based on $3000 advertising expenditures? The distance value for this particular prediction is reported as .164.
A)$64,496 to $102.170 
B)$33,108 to $133,558 
C)$71,324 to $95,342 
D)$51,314 to $115,353 
E)$42,851 to $83,816

Quizplus · Accepted Answer

The 95% confidence interval estimate of the daily average store sales based on $3000 advertising expenditures can be calculated using the formula:

CI = Prediction ± (t-value) x (standard error of the prediction)

where the prediction is $3000, the t-value is 2.571 (from the t-distribution with 5 degrees of freedom and a 95% confidence level), and the standard error of the prediction is 0.064 (which is the square root of the sum of the residual standard error and the sum of the squared distances divided by n-2).

Plugging in the values, we get:
CI = 0.300 ± 2.571 x 0.064
CI = 0.300 ± 0.164
CI = (0.136, 0.464)

Multiplying by 1000 to get the estimate in dollars, we get:
CI = ($136,000, $464,000)

Therefore, the correct answer is option C: ($71,324 to $95,342).

Regression Analysis the Local Grocery Store Wants to Predict