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 3 years ago

The simple linear regression of the data on $Sales and number of customers produced the following...

The simple linear regression of the data on $Sales and number of customers produced the following ANOVA output: ANOVA Source df SS MS F Significance F Regression 46833541 Residual Total 51360495 Complete as much of the ANOVA table as you need to answer the following two questions (Questions 18 and 19): The calculated value of the test statistic used to test the following null and alternative hypotheses Ho: The overall regression model is not significant Ha: The overall regression model...

For data DEMOG, fit three simple linear regression models of the per capita income on each...

For data DEMOG, fit three simple linear regression models of the per capita income on each of the three predictor variables. Does a linear regression model appear to provide a good fit for each of the three predictor variables? Use all appropriate tests, descriptive measures, and plots to conclude your findings here. Which predictor variable leads to significant effect on the per capita income? usborn cap.income home pop Alabama 0.98656 21442 75.9 4040587 Alaska 0.93914 25675 34.0 550043 Arizona 0.90918...

A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from...

A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from depth of the dive (in meters) from a sample of 45 penguins' diving depths and times. Calculate the F-statistic for the regression by filling in the ANOVA table. SS df MS F-statistic Regression Residual 1628.4056 Total 367385.9237

Develop a simple linear regression model to predict the price of a house based upon...

Develop a simple linear regression model to predict the price of a house based upon the living area (square feet) using a 95% level of confidence. Write the reqression equation Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence. Interpret the...

In a simple linear regression, if we scale the data by a negative number, does the...

In a simple linear regression, if we scale the data by a negative number, does the t-statistic for the slope change to be the negative of the original result and the p-value for the slope change because the t-statistic for the slope changes?

Develop a simple linear regression model to predict a person’s income (INCOME) based on their age...

Develop a simple linear regression model to predict a person’s income (INCOME) based on their age (AGE) using a 95% level of confidence. a. Write the regression equation. Discuss the statistical significance of the model as whole using the appropriate regression statistic at a 95% level of confidence. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence. Interpret the coefficient for the independent variable. What percentage of...

. Develop a simple linear regression model to predict a person’s income (INCOME) based upon their...

. Develop a simple linear regression model to predict a person’s income (INCOME) based upon their years of education (EDUC) using a 95% level of confidence. a. Write the reqression equation. b. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence. c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence. d. Interpret the coefficient...

4. Compare the preceding four simple linear regression models to determine which model is the preferred...

4. Compare the preceding four simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection. 5.. Calculate the predicted income of a 45 year old, with 18 years of education, 2 children, and works 40 hours per week using your preferred regression model from part 4. INCOME AGE EARNRS EDUC CHILDS HRS1 500 27...

Consider the simple linear regression mode

Consider the simple linear regression modelYi = β0 + β1xi + εi, where the errors εi are identically and independently distributed as N (0, σ2).(a) If the predictors satisfy x ̄ = 0, show that the least squares estimates βˆ0 and βˆ1 are independently distributed.(b) Let r be the sample correlation coefficient between the predictor and response. Under what conditions will we have βˆ1 = r?(c) Suppose that βˆ1 = r, as in part b), but make no assumptions on...

Discuss the application of simple linear regression

Question