Cleveland Clothing Store is interested in investing in adver

Cleveland Clothing Store is interested in investing in advertising to increase their sales. They consider 4 different channels of advertisement: TV, radio, print, and other (i.e. social media). They want to find the relationship between the amount spent in each advertisement type and the sales amount.They take measurements for 18 days and the data is given below:

1) Least squares prediction:

b0=

b1=

b2=

b3=

b4=

2) y hat =

3) Is the overall regression model significant? (Is at least one of the population regression parameters significant?)

H0: (Click to select)

Ha: At least one of 1, 2,…, 4 0

Test statistic: (2 decimal points)

Critical value: (2 decimal points)

At/With 95% confidence we (Click to select) that the overall regression relationship between the amount of investment in TV, the amount of investment in radio, the amount of investment in print, the amount of investment in other type of advertisements and the sales amount is significant.

This means (Click to select) is/are not zero.

4) Test the significance of the following independent variables

a) Testing the significance of the amount of investment in TV advertisements

Test statistic: (4 decimals)

Critical Value: (4 decimals)

At/With 95% confidence we (Click to select) conclude that the population regression parameter 1 is not zero.(The population parameter for TV advertisements is (Click to select)

b) Testing the significance of the amount of investment in radio advertisements

Test statistic: (4 decimals)

We have (Click to select) evidence that the relationship between the amount of investment in radio advertisement and the sales amount is significant.

c) Testing the significance of other type of advertisements

At/With 95% confidence we (Click to select) conclude that the population regression parameter 3 is not zero.(The population parameter other type of advertisements is (Click to select))

5) After the number of independent variables and the sample size accounted for, what percentage of the variation in sales is explained by the amount of investments in TV, radio, print and other type of advertisements?

% (1 decimal)

6) \"The mean sales for all possible scenarios with x1=50, x2=40,x3=10,x4=6 is between $13,911.8 and $22,752.4\". This statement is explaining (Click to select)

1) Using the same data from question 1 (Cleveland Clothing store) what is the best regression model using stepwise regression? (If a variable is not included bj for that variable is 0.0000.) (4 decimals)

b0

b1(TV)

b2(radio)

b3(print)

b4(other)

2) Using the same data from question 1 (Cleveland Clothing store) what is the best regression model using all possible regressions? (If a variable is not included bj for that variable is 0.0000.) (4 decimals)

b0

b1(TV)

b2(radio)

b3(print)

b4(other)

$1000s	$1000s	$1000s	$1000s	$1000s
Row	sales	tv	radio	print	other
1	18.4	48.4	34.9	14.9	8.4
2	21.8	55.4	23.8	12.1	9.7
3	21.6	56.6	20.6	11.9	7.9
4	33.8	61.6	14.1	17.5	9.9
5	20.9	49.4	28.6	10.9	8
6	15.9	47.4	27.9	12.4	7.9
7	49.5	72.8	43.4	13.1	11.4
8	26.7	59.9	13.7	14.7	9.8
9	28.7	58.3	27.3	9.8	9.1
10	19.7	51.8	22.9	21.1	8.8
11	45.8	65.1	39	29.4	12.3
12	54.4	68.2	41.4	32.7	14.3
13	18.9	49.9	31	13.5	6.8
14	11.4	45.5	24.8	16.6	5.8
15	28.9	55.4	18.2	19	9.8
16	28.6	57.3	14.6	22.8	11
17	41.9	63.5	37.9	34.2	13.5
18	49.2	71.1	23.1	13.6	11.5

Solution

Cleveland Clothing Store is interested in investing in advertising to increase their sales. They consider 4 different channels of advertisement: TV, radio, print, and other (i.e. social media). They want to find the relationship between the amount spent in each advertisement type and the sales amount.They take measurements for 18 days and the data is given below:

Regression Analysis

R²

0.968

Adjusted R²

0.958

n

18

R

0.984

k

4

Std. Error

2.678

Dep. Var.

sales

ANOVA table

Source

SS

df

MS

F

p-value

Regression

2,800.8185

4  

700.2046

97.60

1.47E-09

Residual

93.2665

13  

7.1743

Total

2,894.0850

17  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=13)

p-value

95% lower

95% upper

Intercept

-55.5036

5.4890

-10.112

1.58E-07

-67.3618

-43.6454

tv

1.1727

0.1835

6.3908

2.38E-05

0.7763

1.5691

radio

0.1920

0.0760

2.5257

.0253

0.0278

0.3563

print

0.1614

0.1625

0.9935

.3386

-0.1896

0.5125

other

0.9843

0.9019

1.0914

.2949

-0.9641

2.9327

Predicted values for: sales

95% Confidence Interval

95% Prediction Interval

tv

radio

print

other

Predicted

lower

upper

lower

upper

50

40

10

6

18.3321

13.9118

22.7524

11.0504

25.6138

b0

-55.5036

b1

1.1727

b2

0.1920

b3

0.1614

b4

0.9843

2) y hat = -55.5036+1.1727*tv+0.1920*radio+0.1614*print+0.9843*other

3) Is the overall regression model significant? (Is at least one of the population regression parameters significant?)

H0: (Click to select) 1= 2= 3=4=0

Ha: At least one of 1, 2,…, 4 0

Test statistic: (2 decimal points) = 97.60

Critical value: (2 decimal points) = 3.18

At/With 95% confidence we (Click to select) that the overall regression relationship between the amount of investment in TV, the amount of investment in radio, the amount of investment in print, the amount of investment in other type of advertisements and the sales amount is significant.

This means At least one of 1, 2,…, 4 is/are not zero.

4) Test the significance of the following independent variables

a) Testing the significance of the amount of investment in TV advertisements

Test statistic: (4 decimals)=6.3908

Critical Value: (4 decimals) =2.1604

At/With 95% confidence we ((sufficient) conclude that the population regression parameter 1 is not zero.(The population parameter for TV advertisements is significant

b) Testing the significance of the amount of investment in radio advertisements

Test statistic: (4 decimals) =2.5257

We have (sufficient ) evidence that the relationship between the amount of investment in radio advertisement and the sales amount is significant.

c) Testing the significance of other type of advertisements

test statistic=0.9935

At/With 95% confidence we in sufficient conclude that the population regression parameter 3 is not zero.(The population parameter other type of advertisements is (not significant))

5) After the number of independent variables and the sample size accounted for, what percentage of the variation in sales is explained by the amount of investments in TV, radio, print and other type of advertisements?

% (1 decimal) 96.8

6) \"The mean sales for all possible scenarios with x1=50, x2=40,x3=10,x4=6 is between $13,911.8 and $22,752.4\". This statement is explaining (Click to select)

2) Using the same data from question 1 (Cleveland Clothing store) what is the best regression model using stepwise regression? (If a variable is not included bj for that variable is 0.0000.) (4 decimals)

b0               -58.6829

b1(TV)        1.3493

b2(radio)     0.1956

b3(print)     0.3032

b4(other)   0.0000

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-58.6829

4.6839

-12.5286

0.0000

-68.7289

-48.6369

tv

1.3493

0.0871

15.4822

0.0000

1.1623

1.5362

print

0.3032

0.0982

3.0877

0.0080

0.0926

0.5139

radio

0.1956

0.0765

2.5574

0.0228

0.0316

0.3596

Regression Analysis
	R²	0.968
	Adjusted R²	0.958	n	18
	R	0.984	k	4
	Std. Error	2.678	Dep. Var.	sales
ANOVA table
Source	SS	df	MS	F	p-value
Regression	2,800.8185	4	700.2046	97.60	1.47E-09
Residual	93.2665	13	7.1743
Total	2,894.0850	17
Regression output				confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	-55.5036	5.4890	-10.112	1.58E-07	-67.3618	-43.6454
tv	1.1727	0.1835	6.3908	2.38E-05	0.7763	1.5691
radio	0.1920	0.0760	2.5257	.0253	0.0278	0.3563
print	0.1614	0.1625	0.9935	.3386	-0.1896	0.5125
other	0.9843	0.9019	1.0914	.2949	-0.9641	2.9327
Predicted values for: sales
					95% Confidence Interval	95% Prediction Interval
tv	radio	print	other	Predicted	lower	upper	lower	upper
50	40	10	6	18.3321	13.9118	22.7524	11.0504	25.6138