Sales (thousands of dollars) Year Population Advertising (thousands of dollars) Previous advertising (thousands of dollars) $15713 1 102558 $20 $30 $12937 2 101792 $15 $20 $12872 3 104347 $25 $15 $16227 4 106180 $30 $25 $15388 5 106562 $15 $30 $13180 6 105209 $25 $15 $17199 7 109185 $35 $25 $20674 8 109976 $40 $35 $20350 9 110659 $20 $40 $14444 10 111844 $25 $20 Consider the model: salest = 0 + 1t + 2popt + 3advt + 4advt-1 + t where salest = sales in year t, popt = size of the population residing within 10 kilometres of the restaurant, advt = advertising expenditures in year t, and advt-1 = advertising expenditures in the previous year. Based on the sample data, a regression analysis was performed and the results are shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0,994630788 R Square 0,989290405 Adjusted R Square 0,980722728 Standard Error 393,1191142 Observations 10 ANOVA df SS MS F Significance F Regression 4 71378769,21 17844692,3 115,4677605 4,12255E-05 Residual 5 772713,1899 154542,638 Total 9 72151482,4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 24799,62737 17008,82164 1,458045001 0,204627778 -18922,94058 68522,19531 Year 318,9594603 178,6691756 1,785195791 0,134293268 -140,3242772 778,2431977 Population -0,20186378 0,172483261 -1,17033838 0,294606217 -0,645246117 0,241518557 Advertising 134,947818 19,58889716 6,888995176 0,000986635 84,59295482 185,3026813 Previous_Advertising 295,5352939 19,53921967 15,12523524 2,2891E-05 245,3081307 345,762457 You are required to answer the following questions: Estimate the sample regression equation. What proportion of variation in annual sales is explained by variation in year, population size, advertising expenditure for current year and advertising expenditure for previous year? Construct a 99% confidence interval for From this confidence interval, can you conclude that previous year advertising expenditure influence current year sales? Test at 5% level of significance the hypothesis that year, population size, advertising expenditure for current year and advertising expenditure for previous year jointly influence annual sales.

Sales (thousands of dollars) Year Population Advertising (thousands of dollars) Previous advertising (thousands of dollars) $15713 1 102558 $20 $30 $12937 2 101792 $15 $20 $12872 3 104347 $25 $15 $16227 4 106180 $30 $25 $15388 5 106562 $15 $30 $13180 6 105209 $25 $15 $17199 7 109185 $35 $25 $20674 8 109976 $40 $35 $20350 9 110659 $20 $40 $14444 10 111844 $25 $20 Consider the model: salest = 0 + 1t + 2popt + 3advt + 4advt-1 + t where salest = sales in year t, popt = size of the population residing within 10 kilometres of the restaurant, advt = advertising expenditures in year t, and advt-1 = advertising expenditures in the previous year. Based on the sample data, a regression analysis was performed and the results are shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0,994630788 R Square 0,989290405 Adjusted R Square 0,980722728 Standard Error 393,1191142 Observations 10 ANOVA df SS MS F Significance F Regression 4 71378769,21 17844692,3 115,4677605 4,12255E-05 Residual 5 772713,1899 154542,638 Total 9 72151482,4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 24799,62737 17008,82164 1,458045001 0,204627778 -18922,94058 68522,19531 Year 318,9594603 178,6691756 1,785195791 0,134293268 -140,3242772 778,2431977 Population -0,20186378 0,172483261 -1,17033838 0,294606217 -0,645246117 0,241518557 Advertising 134,947818 19,58889716 6,888995176 0,000986635 84,59295482 185,3026813 Previous_Advertising 295,5352939 19,53921967 15,12523524 2,2891E-05 245,3081307 345,762457 You are required to answer the following questions: Estimate the sample regression equation. What proportion of variation in annual sales is explained by variation in year, population size, advertising expenditure for current year and advertising expenditure for previous year? Construct a 99% confidence interval for From this confidence interval, can you conclude that previous year advertising expenditure influence current year sales? Test at 5% level of significance the hypothesis that year, population size, advertising expenditure for current year and advertising expenditure for previous year jointly influence annual sales.

Name: The owner of a restaurant in Bloomington, Indianna, has recorded sales
Uploaded: 2024-03-20T07:07:12.000Z
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Description: The owner of a restaurant in Bloomington, Indianna, has recorded sales data for the past 10 years. He has also recorded data on potentially relevant variables. The following table gives data on sales and other potentially relevant variables for that

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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The owner of a restaurant in Bloomington, Indianna, has recorded sales data for the past 10 years. He has also recorded data on potentially relevant variables. The following table gives data on sales and other potentially relevant variables for that particular restaurant.

Sales (thousands of dollars)	Year	Population	Advertising (thousands of dollars)	Previous advertising (thousands of dollars)
$15713	1	102558	$20	$30
$12937	2	101792	$15	$20
$12872	3	104347	$25	$15
$16227	4	106180	$30	$25
$15388	5	106562	$15	$30
$13180	6	105209	$25	$15
$17199	7	109185	$35	$25
$20674	8	109976	$40	$35
$20350	9	110659	$20	$40
$14444	10	111844	$25	$20

Consider the model: sales_t= ₀ + ₁t + ₂pop_t + ₃adv_t + ₄adv_t-1 + _t

where sales_t= sales in year t,

pop_t = size of the population residing within 10 kilometres of the restaurant,

adv_t = advertising expenditures in year t, and

adv_t-1 = advertising expenditures in the previous year.

Based on the sample data, a regression analysis was performed and the results are shown below.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0,994630788
R Square	0,989290405
Adjusted R Square	0,980722728
Standard Error	393,1191142
Observations	10

ANOVA
	df	SS	MS	F	Significance F
Regression	4	71378769,21	17844692,3	115,4677605	4,12255E-05
Residual	5	772713,1899	154542,638
Total	9	72151482,4

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	24799,62737	17008,82164	1,458045001	0,204627778	-18922,94058	68522,19531
Year	318,9594603	178,6691756	1,785195791	0,134293268	-140,3242772	778,2431977
Population	-0,20186378	0,172483261	-1,17033838	0,294606217	-0,645246117	0,241518557
Advertising	134,947818	19,58889716	6,888995176	0,000986635	84,59295482	185,3026813
Previous_Advertising	295,5352939	19,53921967	15,12523524	2,2891E-05	245,3081307	345,762457

You are required to answer the following questions:

Estimate the sample regression equation.
What proportion of variation in annual sales is explained by variation in year, population size, advertising expenditure for current year and advertising expenditure for previous year?
Construct a 99% confidence interval for From this confidence interval, can you conclude that previous year advertising expenditure influence current year sales?
Test at 5% level of significance the hypothesis that year, population size, advertising expenditure for current year and advertising expenditure for previous year jointly influence annual sales.

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