Final answer:
a. Correct. If the floor space of a store were to increase by one square foot, the predicted increase in sales would be $2,050. b. Not correct. If a store has a floor space of 75 square feet, the predicted sales in a day is not $6,100. c. Correct. If a store has a floor space of 175 square feet, the predicted sales in a day is $11,500.
Step-by-step explanation:
a. Correct
If the floor space of a store were to increase by one square foot, the predicted increase in sales would be $2,050. This is because the coefficient of the x term in the regression equation is 54, which means that for each additional square foot of floor space, the predicted sales increase by $54. Therefore, if the floor space increases by one square foot, the predicted increase in sales would be 1 * 54 = $54. Adding this to the y-intercept of $2,050 gives a total predicted increase in sales of $2,050 + $54 = $2,104.
b. Not correct
If a store has a floor space of 75 square feet, the predicted sales in a day is $6,100. This conclusion is not correct because it involves extrapolation, which means predicting outside the range of the data. The regression equation was developed using data for floor spaces ranging from 100 square feet to 300 square feet. Therefore, using the equation to predict sales for a store with a floor space of 75 square feet is not valid.
c. Correct
If a store has a floor space of 175 square feet, the predicted sales in a day is $11,500. This conclusion is correct based on the regression equation. By substituting x = 175 into the equation y^ = 2,050 + 54x, we can calculate the predicted sales: y^ = 2,050 + 54 * 175 = 2,050 + 9,450 = $11,500.