Observations are taken on sales of a certain mountain bike in 30 sporting goods
ID: 3178715 • Letter: O
Question
Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars). X_1 = display floor space (square meters), X_2 = competitors' advertising expenditures (thousands of dollars), X_3 = advertised price (dollars per unit). Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) The coefficient of FloorSpace says that each additional square foot of floor space takes away 0.1496 from sales (in thousands of dollars). Adds about 11.29 to sales (in thousands of dollars). takes away 11.29 from sales (in thousands of dollars). Adds about 6.889 to sales (in thousands of dollars). The coefficient of CompetingAds says that each additional $1,000 of "competitors' advertising expenditures" takes away 11.29 from sales (in thousands of dollars). reduces sales by about 6.889 from sales (in thousands of dollars). takes away 0.1406 from sales (in thousands of dollars). Adds about 6.889 to sales (in thousands of dollars). The coefficient of Price says that each additional $1 of advertised price reduces sales by about 0.1446 from sales (in thousands of dollars). reduces sales by about 6.889 from sales (in thousands of dollars). takes away 11.29 from sales (in thousands of dollars). Adds about 6.889 to sales (in thousands of dollars). The intercept is not meaningful, since a mountain bike cannot sell for zero, which will happen if all the variables are zero. False True Make a prediction for Sales when FloorSpace = 84, CompetingAds = 88, and Price = 1.138. (Enter your answer in thousands. Round your answer to 2 decimal places.)Explanation / Answer
a) The fitted regression equation from the given equation is:
1263.91 + 11.29* Floor Space - 6.889 * Competing Ads - 0.1446* Price
b-1) Now we know from the above equation, each additional square meter of floor space would add 11.29 thousands of sales. Therefore b) adds 11.29 to the sales ( in thousands of dollars ) is the correct answer.
b-2) From the equation again we get as the coefficient is negative, increase in $1000 of competitors advertisement expenditure decreases our sales by 6.889 thousand of sales. Therefore b) reduces 6.889 thousand of sales is the correct answer.
b-3) Additional $1 of advertised price decreases the sales by 0.1446 thousand dollars as the coefficient is -0.1446. a) is the correct answer.
c) The given statement is false, because if their is no change in the independent variables like price, competitors advertisement price, and floor space, the base price will be the intercept = 1263.91.
d) Prediction for sales for the given values:
Sales = 1263.91 + 11.29* Floor Space - 6.889 * Competing Ads - 0.1446* Price
Sales = 1263.91 + 11.29*84 - 6.889*88 - 0.1446*1138 = 1263.91 + 948.36 - 606.232 - 164.5548
Sales = 1441.4832
Therefore the sales prediction would be $1441.48 thousands of dollars.
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