Question

C 3 of 7 ID: MST.MR.CM.01.0060 [14 points) Joe Smith is considering opening a franchise of a very popular gourmet fruit drink store. He is interested in constructing a multiple regression model to predict the number of drinks sold in a day based upon the volume of foot traffic passing the store, the daily maximum temperature and the average drink price. Information has been collected on 30 randomly selected days for several randomly chosen stores: show data a) Find the multiple regression equation using all three explanatory variables. Assume that x1 is volume of traffic, X2 is maximum daily temperature and x3 is average drink price. Give your answers to 3 decimal places. y = + vol. traffic + max temp + average drink price b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis rejected. c) The value of R2 for this model, to 3 decimal places, is equal to d) The value of s for this model, to 3 decimal places, is equal to e) The least significant explanatory variable in this model is: vol. traffic max temp average drink price f) Construct a new multiple regression model by removing the variable average drink price. Give your answers to 3 decimal places. The new regression model equation is: = + vol. traffic + max temp g) In the new model compared to the previous one, the value of R2 (to 3 decimal places) is: increased decreased unchanged h) In the new model compared to the previous one, the value of s (to 3 decimal places) is: increased decreased unchanged i) The better model the: original model reduced model

Answer 1

Result:

Excel Addon Megastat used.

Regression Analysis
	R²	0.844
	Adjusted R²	0.826	n	30
	R	0.919	k	3
	Std. Error of Estimate	66.071	Dep. Var.	y
Regression output					confidence interval
variables		coefficients	std. error	t (df=26)	p-value	95% lower	95% upper
Intercept	a =	103.120	71.989	1.432	.1639	-44.855	251.094
vol.traffic	b1 =	1.365	0.122	11.155	0.0000	1.114	1.617
max temp	b2 =	0.274	0.126	2.181	.0384	0.016	0.533
average drink	b3 =	23.908	18.510	1.292	.2079	-14.140	61.956
ANOVA table
Source	SS	df	MS	F	p-value
Regression	612,671.894	3	204,223.965	46.78	0.0000
Residual	113,501.473	26	4,365.441
Total	726,173.367	29

a).

y = 103.120+1.365*vol. traffic +0.274*max temp+23.908*average drink price

b).

null hypothesis for F test is rejected.

c).

R square = 0.844

d).

value for s =66.071

e).

least significant explanatory variable =

average drink price

f).

Regression Analysis
	R²	0.834
	Adjusted R²	0.821	n	30
	R	0.913	k	2
	Std. Error of Estimate	66.884	Dep. Var.	y
Regression output					confidence interval
variables		coefficients	std. error	t (df=27)	p-value	95% lower	95% upper
Intercept	a =	167.906	52.272	3.212	.0034	60.652	275.159
vol.traffic	b1 =	1.374	0.124	11.103	0.0000	1.120	1.628
max temp	b2 =	0.269	0.127	2.111	.0442	0.008	0.530
ANOVA table
Source	SS	df	MS	F	p-value
Regression	605,389.318	2	302,694.659	67.66	0.0000
Residual	120,784.049	27	4,473.483
Total	726,173.367	29

y = 167.906+1.374*vol. traffic +0.269*max temp

g).

new value of R square =0.834

decreased

h).

new value of s=66.884

increased

i).

the better model is

original model.