The owners of a chain of ice cream stores has the business objective of improvin

Question

The owners of a chain of ice cream stores has the business objective of improving the forecast of daily sales so that staffing shortages can be minimized during the summer season. As a starting? point, the owners decide to develop a simple linear regression model to predict daily sales based on atmospheric temperature. They select a sample of 15 consecutive days. The results are shown in the accompanying table. Complete? (a) through? (e).

a. Assuming a linear? relationship, use the? least-squares method to compute the regression coefficients b0 and b1.

b0 = ?

b1 = ?

(Round to 4 decimal places)

b. Predict the sales for a day in which the temperature is 76 F.

c. Plot the residuals versus the time period.

d. Compute the? Durbin-Watson statistic. At the 0.05 level of? significance, is there evidence of positive autocorrelation among the? residuals?

D = ?

Use the table to find the critical values of the? Durbin-Watson statistic.

dL = ?

dU = ?

Is there evidence of positive autocorrelation among the? residuals?

YES OR NO?

Day Sales ($1,000) Temp (F) 1 1.55 61 2 1.65 71 3 1.96 75 4 1.79 73 5 2.02 75 6 2.31 79 7 2.16 82 8 2.68 84 9 2.93 89 10 3.18 89 11 3.06 90 12 3.29 93 13 3.38 97 14 2.87 86 15 2.56 83 Y (76) =

Explanation / Answer

a)
Regression line equation: y=44.688692285389+14.888195124878x

b0 = 44.6887

b1 = 14.8882

b)

Y(76) = $1176.1915

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