Question

Price($)	Promotional Exp (K)	Quality	City: 1/Suburban: 0	Sales(K)
949	5	100	1	168
941	4.3	94	1	150
934	3	89	1	168
921	2	85	1	148
915	0.75	79	1	152
909	4.8	75	1	162
904	3.6	70	1	160
1014	3	63	0	123
1006	1.5	60	0	130
990	0.7	55	0	116
978	4.7	51	1	142
962	3.5	47	1	145
955	2.8	42	1	134
953	1.3	35	0	128
1050	0.25	30	0	117
1040	4.5	26	0	118
1038	3.2	22	0	107
1022	2.4	17	0	124
1021	1.2	12	0	104
1018	0	6	0	106
1010	2.9	60	0	120
935	4.4	91	1	153

Case Study

Please consider the data presented above for the monthly sales of Ever-cool brand of refrigerators in 1,000s of dollars (Dependent Variable) and the four independent variables.

Independent variables are:

Price (in dollars); Promotional Expenditure (in 1,000s of dollars); Quality of service (scale of 1-100); location (categorical variable: city area: 1; suburban area: 0).

Develop a multiple linear regression equation using either Excel or Minitab and based on the relevant outputs please answer the following questions:

a. Based on the relevant residual and normality plots, do you see any evidence of violation of assumptions (Linearity, Normality, Equal variance)? You must attach the relevant plots as part of your report.

b. State the multiple regression equation and interpret the statistical meaning of the estimated slopes, b₁, b₂, b₃, and b₄ (corresponding to the four independent variables).

c. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Based on these results, indicate the independent variable(s) to include in this model. (Based on t - test results)

d. Construct a 95% confidence interval estimate of the population slope between the independent variable ‘Quality’ and the dependent variable ‘Monthly Sales’ (B3) (please note that Minitab can’t do this directly, however you may use the relevant information from Minitab output and then construct the confidence interval manually)

e. Perform the overall F- test and comment on the significance of the model.

Please follow the following instructions:

• Use Excel/ or Minitab to run the analysis.
• Copy/Paste Excel/ or Minitab results to justify your answers.
• submit original Excel/or minitab results along with your answers

Answer 1

Let the dependent variable, Y = Sales, and the independent variables, x1 = Price, x2 = Promotional Exp, x3 = Quality, and x4 = City

The regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Hours' column, Input X Range: 'Feet and Large' column, Click on Residual plot and Normal Probability Plot then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

a)

Linearity

From the line fit plot (scatter plot), there is a linear trend which indicates that the normality assumption is met.

Normality

From the normal probability plot, the residual values are along the straight line which indicates that the normality assumption is met.

Equality of variance

From the normal probability plot, the residual values are randomly distributed along the horizontal line which indicates that the equality of variances assumption is met.

b)

From the regression summary report

	Coefficient	Interpretation
x1	-0.136	For 1 unit increase in price, the sales decrease by 0.136
x2	1.759	For 1 unit increase in promotional experience, the sales increase by 1.759
x3	0.241	For 1 unit increase in quality, the sales increase by 0.241
x4	12.286	If suburban, the sales increase by 12.286

c)

From the regression summary report

	P-value
x1	0.086	<	0.05	Significant
x2	0.187	>	0.05	Not Significant
x3	0.014	<	0.05	Significant
x4	0.089	>	0.05	Not Significant

Hence only variable x1 and x3 should be included

d)

From the regression summary report, the 95% CI for the coefficient estimate of Quality is,

	Lower 95%	Upper 95%
Quality	0.054963	0.426603

e)

From the regression summary report,

	Significance F
Regression	2.31294E-08

The significance F value is 0.0000 which is less than 0.05 at a 5% significance level which mean the model fits the data value at the 5% significance level. Hence we can conclude that independent variables fit the model significantly compared to intercept only model.