A media company wants to use the number of minutes a commercial is broadcasted on TV (X) to predict the number of sales (Y). Data comprising 1,000 brands using commercials was used to fit the model:

E(Y) = 0 + 1X

The results of the simple linear regression were:

i = 500 + 20Xi

1) Interpret the estimate of 0, the Y-intercept of the line. (a) For every minute extra the commercial is broadcasted, it is expected an increase in sales by 20 units on average. (b) About 95% of minutes broadcasted fall within 500 of the least squares line. (c) Companies will sell at least 500 units. (d) There is no practical interpretation.2) Interpret the estimate of 1, the slope of the line. (a) Number of minutes a commercial is broadcasted and sales are non-related variables. (b) Companies will sell at least 500 units. (c) For every minute extra the commercial is broadcasted, it is expected an increase in sales by 20 units on average. (d) There is no practical interpretation.

QM461, Trimester 1 2015

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3) If the two-tail p-value for testing 1 is 0.01, interpret this p-value for testing whether 1 exceeds 0. (a) Number of minutes a commercial is broadcasted is a poor predictor of sales. (b) For every additional minute a commercial is broadcasted, it is expected an increase in sales by 20 units on average. (c) There is insufficient evidence (at = 0.10) to conclude that minutes a commercial is broadcasted (X) is a useful linear predictor of sales (Y). (d) There is sufficient evidence (at = 0.05) to conclude that minutes a commercial is broadcasted (X) is a useful linear predictor of sales (Y)