A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the model:Sales = β0 +β1 Advertising + ε. The following ANOVA table shows a portion of the regression results. dfSSMSFRegression178.5378.533.58Residual23504.0221.91 Total24582.55 CoefficientsStandard Errort-statp-valueIntercept40.1014.082.8480.0052Advertising2.881.521.8950.0608 If the significance level is 0.05 (α=0.05), which of the following is true about the hypothesis of β1? OOOReject Ho: B1=0 and conclude that the slope is significantly not equal to zero.Accept Ho: B₁-0 and conclude that the slope is equal to zero.Reject Ho: 31=0 and conclude that the slope is equal to zero.Fail to reject Ho: P₁=0 and do not have sufficient evidence to conclude the slope is not equal to zero.

The regression equation Y = Bo + B1x ; Where, B1 is the slope The slope of the regression equation tells you that, if the x factor increases by then the corresponding response factor would decrease (or) increase by slope (B1) value. Null hypothesis Ho : The regression slope is equal to zero. i.e., β1 = 0 Alternative hypothesis Ha : The regression slope is not equal to zero. i.e., β1 # 0 Output : From the above output, the P -value of the Advertising estimate is 0.0608 We have significance level α=0.05 Rejection rule : Reject Ho if P - value < α level Fail to reject Ho if P - value > α level Conclusion : The P value (0.0608) > α level (0.05). Therefore, as per rejection rule we should not reject the null hypothesis Ho at 0.05 level of significance. Failing to reject Ho means, regression slope is equal to zero. Hence the conclusion is, Option (D) : Fail to reject Ho : β1 = 0 and do not have sufficient evidence to conclude that the slope is not equal to zero.

Answered: A marketing analyst wants to examine…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

	df	SS	MS	F
Regression	1	78.53	78.53	3.58
Residual	23	504.02	21.91
Total	24	582.55
	Coefficients	Standard Error	t-stat	p-value
Intercept	40.10	14.08	2.848	0.0052
Advertising	2.88	1.52	1.895	0.0608