Question

A pizza company has asked you for your assistance in developing a model that predicts the demand for the new snack pizza named Pizza1. This product competes in a market with another brand that is named B2 for identification. At present, the products are sold by three major distribution chains identified as​ 1, 2, and 3. These three chains have different market​ sizes, and,​ thus, sales for each distributor are likely to be different. The accompanying data table contains randomly sampled weekly observations from the three distribution chains. Use multiple regression to develop a model that predicts the quantity of Pizza1 sold per week. The model should contain only important predictor variables.

Sales of Pizza1   Price of Pizza1   Distributor   Price of B2
6,543   0.66   1   0.82
10,125   0.62   1   0.80
10,609   0.62   1   0.77
8,509   0.62   1   0.66
10,655   0.63   1   0.65
6,773   0.69   1   0.63
18,888   0.63   1   0.65
11,761   0.65   1   0.78
4,614   0.77   1   0.62
13,562   0.88   2   0.80
14,555   0.84   2   0.93
13,165   0.87   2   0.75
13,034   0.88   2   0.74
12,921   0.92   2   0.79
11,026   0.93   2   0.76
14,448   0.84   2   0.78
511   0.67   3   0.65
573   0.66   3   0.65
610   0.67   3   0.65
461   0.66   3   0.57
498   0.66   3   0.57
501   0.65   3   0.59
507   0.67   3   0.65

Use technology to estimate a model with the variables selected above. Give the equation for the regression line.

y^{^}= (.....) + (....)(PriceofPizza1) + (....)(D2) + (....)(D3)

Answer 1

Using the regression function from the data analysis package in the MS-Excel,

Following summary output is obtained :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.790760728
R Square	0.62530253
Adjusted R Square	0.566139771
Standard Error	3921.483481
Observations	23
ANOVA
	df	SS	MS	F	Significance F
Regression	3	487600121.4	1.63E+08	10.56919159	0.000261709
Residual	19	292182621.2	15378033
Total	22	779782742.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-12032.94712	7887.137817	-1.52564	0.143573356	-28540.9163	4475.022049	-28540.9163	4475.022049
Prize of Pizza1	25383.35103	9272.191508	2.737578	0.013082379	5976.431164	44790.27089	5976.431164	44790.27089
Distributor	-3626.061081	1125.726048	-3.22109	0.004496415	-5982.232779	-1269.889384	-5982.232779	-1269.889384
Price of B2	11531.6939	11639.34231	0.990751	0.334257544	-12829.72953	35893.11732	-12829.72953	35893.11732

In general, the multiple linear regression equation is given as : = b0 + b1 * x1 + b2 * x2 + b3 * x3

With respect to the above table, b0 = -12032.94712 , b1 = 25383.35103 , b2 = -3626.061081 and

b3 = 11531.6939.

And x1 repesents the " Prize of Pizza1 ", x2  repesents the " Distributor " and the

x3 repesents the " Price of B2 "

Therefore, the multiple linear regression equation is :

= -12032.94712 + 25383.35103* x1 - 3626.061081 * x2 + 11531.6939* x3