Question

Denote Y for profit (in dollars) and X for price (in dollars). The linear regression model of Y on X is Y_i= β₀ + β₁X_i + ε_i (i=1, 2, … n) for n pairs on Y and X. The hypothesis H₀: β₁=0 vs H₁: β₁≠0 at α=0.01. The fitted model through least squares techniques from a random sample of 81 is: = 0.75 - 1.15X. If H₀ is accepted, the true statement (s) is/are for the regression model:

       a. The model can’t be used to forecast profit

       b. None of the statements in a, c, d are true

       c. The expected increase in profit for each dollar decrease in price will be $1.15

       d. There is high linear correlation between profit and price

Answer 1

Option a.

The model can't be used to forecast.

(Since we accepted H0 : 1 = 0, where 1 is coeffcient of X(price) in model, we conclude that the price is not significantly affecting the profit or the price does not predict profit significantly.

This means that price has very low(no significant) contribution in predicting profit.

Hence the model cannot be used to forecast the value of profit.)