develop simple linear regression models for predicting sales as a function of the number of each...

develop simple linear regression models for predicting sales as a function of the number of each type of ad. Compare these results to a multiple linear regression model using both independent variables. State each model and explain R- square, significance F and P-values.

Concert Sales
	Thousands of	Thousands of
Sales ($1000)	Radio&TV ads	Newspaper ads
$1,119.00	0	40
$973.00	0	40
$875.00	25	25
$625.00	25	25
$910.00	30	30
$971.00	30	30
$931.00	35	35
$1,177.00	35	35
$882.00	40	25
$982.00	40	25
$1,628.00	45	45
$1,577.00	45	45
$1,044.00	50	50
$914.00	50	50
$1,329.00	55	20
$1,330.00	55	20
$1,405.00	60	30
$1,436.00	60	30
$1,521.00	65	35
$1,741.00	65	35
$1,866.00	70	40
$1,717.00	70	40

Expert Solution

simple linear regression with Sales and Radio & TV adds.

Go to data tab --> choose data analysis and choose regression statistics.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.697
R Square	0.485
Adjusted R Square	0.460
Standard Error	14.551
Observations	22

ANOVA
	df	SS	MS	F	Significance F
Regression	1	3992.393	3992.393	18.85481532	0.00032
Residual	20	4234.879	211.744
Total	21	8227.273

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-5.7008932	11.67721	-0.48821	0.6307	-30.05913327	18.65735	-30.0591	18.65735
Sales ($1000)	0.039899813	0.009189	4.342213	0.0003	0.020732271	0.059067	0.020732	0.059067

simple linear regression with Sales and Newspaper adds

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.264
R Square	0.070
Adjusted R Square	0.023
Standard Error	341.515
Observations	22

ANOVA
	df	SS	MS	F	Significance F
Regression	1	175143.3	175143.3	1.501669	0.235
Residual	20	2332649	116632.5
Total	21	2507793

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	877.2432432	293.084	2.993146	0.007186	265.8807233	1488.606	265.8807	1488.606
Newspaper ads	10.20486486	8.327607	1.225426	0.23465	-7.166218221	27.57595	-7.16622	27.57595

Multiple linear regression:

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.738
R Square	0.544
Adjusted R Square	0.496
Standard Error	245.233
Observations	22

ANOVA
	df	SS	MS	F	Significance F
Regression	2	1365150	682574.9	11.34994	0.0006
Residual	19	1142643	60139.1
Total	21	2507793

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	385.3814221	237.7349	1.621055	0.121484	-112.2035109	882.9664	-112.204	882.9664
Radio&TV ads	12.03232224	2.704913	4.448322	0.000276	6.370874871	17.69377	6.370875	17.69377
Newspaper ads	9.391870119	5.982624	1.569858	0.132952	-3.129904984	21.91365	-3.1299	21.91365

orchestra answered 2 years ago

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