Cleveland Clothing Store is interested in investing in advertising to increase t
ID: 3390705 • Letter: C
Question
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 11.5Explanation / Answer
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
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
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
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
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
other
Predicted
lower
upper
lower
upper
50
40
10
6
18.3321
13.9118
22.7524
11.0504
25.6138
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