Sera Smith, a research analyst, had a hunch that there was a relationship between the percentage change in a firm’s number of salespeople and the percentage change in the firm’s sales during the following period. Smith ran a regression analysis on a sample of 50 firms, which resulted in a slope of 0.72, an intercept of +0.01, and an R-squared value of 0.65. Based on this analysis, if a firm made no changes in the number of sales people, what percentage change in the firm’s sales during the following period does the regression model predict? A) +0.72%. B) +0.65%. C) +1.00%. D) +0.10%. How do you figure this out? How do you know X (independent variable) is equal to 0? Is it possible to compute the SEE?
yancey, Linear regression model Y = beta0+beta1*X In this problem X = percentage change in a firm’s number of salespeople. (“if a firm made no changes in the number of sales people” – X = 0). Y(0)= beta0 = intercept = 0.01 = 1% the answer is C You don’t need to calculate SEE and you can’t from the information given in the problem. If you knew sigma of the dependent variable Y, then it would be: SEE = sqrt(SSE/n-2)=sqrt([1-R^2]*(sigma_Y)^2/n-2)=sigma_Y*sqrt[(1-R^2)/(n-2)]
thank you