Question

The regression equation is

Sales = 0.20 + 2.60 Adbudget

Predictor Coef SE Coef T P

Constant 0.200 2.132 0.09 0.931

Adbudget 2.6000 0.6429 4.04 0.027

S = 2.03306 R-Sq = 84.5% R-Sq(adj) = 79.3%

Analysis of Variance

Source     DF SS MS   F P

Regression 1 67.600 67.600 16.35 0.027

Residual Error 3 12.400 4.133

Total 4 80.000

a) What is the slope of the regression equation?

b) Null and alternative hypothesis

c) Is the slope significantly different than zero?

d) Write a statistical conclusion about the relationship of the two variables

e) Find the coefficient of correlation and interpret

f) Assuming the slope was significantly different than zero, how do you interpret the effect of a one unit increase in Ads budget on Sales for the company?

g) Calculate the predicted value of Sales if Adbudget=5

h) What plot would you recommend before fitting a regression line?

i) Interpret the coefficient of determination

Answer 1

The slope of the regression equation is b 2.600 Null hypothesis: H,:A=0 There is no linear relationship between sales and ad budget Alternative hypothesis: There is a linear relationship between sales and ad budget.

Since p-value (-0.027) a(= 0.05). then reject the null hypothesis. Therefore, the slope is significantly different than zero. There is a significant linear relationship between sales and ad budget. The value of coefficient of correlation is r=Vr"-、/0.845=0.919 Interpretation: There is a strong positive linear relationship between sales and ad budget For each increase of one unit in ad budget, the sales is increased by 2.60

Sales = 0.20 + 260Adbudget = 0.20 +2.60(5) = 0.20+13 = 13.20 The predicted value of Sales if Ad budget-5 is 13.20 Ch). Scatterplot. (i) 84.5% of variation in sales is explained by ad budget.