Question

A division of a multinational retail company prepared a presentation to give at the home office in Paris, France. The presentation includes a scatterplot that shows the relationship between square footage and annual sales in retail outlets owned by the chain. The units in the plot show the size in thousands of square feet and the response in thousands of dollars. A fitted line in the plot is y = 47 + 650x.

(a) Interpret the slope and intercept in the fitted line.
(b) To present the model in Europe, the plot must be shown with sales denominated in euros rather than dollars 1use the exchange rate
$1 = €0.822 and size given in square meters rather than square feet (1 square foot = 0.093 square meter). Find the slope and intercept in these new units.
(c) Would the r2 summary attached to the regression model change along with the slope and intercept when the data are changed into euros and meters?
(d) Would se change with the new scales?

Answer 1

(A) Interpretation is below

(B) The slope in the new units is now 60.45

The intercept in the new units is 38.634

(C) yes

(D) yes

Explanation:

(A) The intercept here is 47. This means that the minimum response or payment is 47 (thousand dollars).

The slope is 650. This means that the change in Y due to a change in X is 650. In other words, if there is a change of 1(thousand square feet), there will be a resulting increase of 650(thousand dollars). It will result in an increase instead of decrease because the slope is positive or bearing a + sign.

(B) The new units are EUROS and SQUARE METRES.

$1 = €0.822

1s.f. = 0.093s.m.

The new fitted line would be:

0.822Y = 47(0.822) + (0.093)(650)X

0.822Y = 38.634 + 60.45X

The slope in the new units is 60.45 and the intercept on the y-axis is 38.634.