Run a multiple linear regression using sales as the dependent variable where qua
ID: 3242925 • Letter: R
Question
Run a multiple linear regression using sales as the dependent variable where quarter is the dummy variable and TV, Radio, and News are the advertising media.
a) Discuss the R^2adj and Radj (to see if this is a feasibly good model)
b) Write out the equation of the model and define all the coefficients.
c) Run an F test.
d) Are any slopes problematic? Which ones? Give some reasons why you think this has occured?
e) Predict the next year of sales if the following are the advertising budgets:
QTR SALES TV RADIO NEWS 1 88 100 95 87 2 80 99 99 98 3 96 101 103 101 4 76 93 95 91 1 80 95 102 88 2 73 95 94 84 3 58 80 89 74 4 116 116 112 102 1 104 106 110 105 2 99 105 87 97 3 64 90 90 88 4 126 113 101 108 1 94 96 100 89 2 71 98 85 78 3 111 109 99 109 4 109 102 101 108 1 100 100 93 102 2 127 107 108 110 3 99 108 100 95 4 82 95 69 90 1 67 91 95 85 2 100 114 91 103 3 78 93 80 80 4 115 115 85 104 1 83 97 105 83Explanation / Answer
First we copy the data in excel where the first variable is SALES.
SALES
QTR
TV
RADIO
NEWS
88
1
100
95
87
80
2
99
99
98
96
3
101
103
101
76
4
93
95
91
80
1
95
102
88
73
2
95
94
84
58
3
80
89
74
116
4
116
112
102
104
1
106
110
105
99
2
105
87
97
64
3
90
90
88
126
4
113
101
108
94
1
96
100
89
71
2
98
85
78
111
3
109
99
109
109
4
102
101
108
100
1
100
93
102
127
2
107
108
110
99
3
108
100
95
82
4
95
69
90
67
1
91
95
85
100
2
114
91
103
78
3
93
80
80
115
4
115
85
104
83
1
97
105
83
We go to Data then Data Analysis, there we select Regression Analysis. We select SALES as Y and for X we select all other dependent variable.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9341
R Square
0.8725
Adjusted R Square
0.8471
Standard Error
7.5010
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
4
7704.0453
1926.0113
34.2306
0.0000
Residual
20
1125.3147
56.2657
Total
24
8829.36
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-107.5938
20.5451
-5.2370
0.0000
-150.4501
-64.7375
QTR
0.5156
1.4954
0.3448
0.7338
-2.6037
3.6350
TV
1.0188
0.2862
3.5603
0.0020
0.4219
1.6157
RADIO
0.1632
0.1904
0.8575
0.4013
-0.2338
0.5603
NEWS
0.8475
0.2576
3.2897
0.0037
0.3101
1.3849
Question a)
The value of R^2 is 0.8725. This value tells us that 87.25% of the variation for the variable SALES is going to be explained by all other independent variables (QTR, TV, RADIO and NEWS).
Here the value of adjusted R^2 is 0.8471; this value help us to compare the explanatory power of regression models that contain different numbers of predictors. In other words we can say that of adjusted R^2 modified version of R-squared which is adjusted for the number of predictors in the model.
Question b)
SALES = -107.5983 + 0.5156*QTR + 1.0188*TV + 0.1632*RADIO + 0.8475*NEWS
If there is one unit of increment for the variable QTR keeping all other variable as constant then the variable SALES is going to be increased by 0.5156 units.
If there is one unit of increment for the variable TV keeping all other variable as constant then the variable SALES is going to be increased by 1.0188 units.
If there is one unit of increment for the variable RADIO keeping all other variable as constant then the variable SALES is going to be increased by 0.1632 units.
If there is one unit of increment for the variable NEWS keeping all other variable as constant then the variable SALES is going to be increased by 0.8475 units.
Question c)
H0: Regression model is insignificant
H1: Regression model is significant
Level of significance = .05
F-test statistics = 34.231
P-value = .0000
Here the p-value is less than he level of significance; the null hypothesis can be rejected at 5% level of significance.
There is sufficient evidence to conclude that the value of the F-test statistics is significant here.
The Regression model is significant here.
Question d)
QTR = 0.7338 (p-value)
RADIO = 0.4013 (p-value)
The t-test p-values for QTR and Radio are very high. If we take the level of significance as 5% then these slopes are insignificant at 5% level of significance.
The slope for the variable Quarter and RADIO are problematic here.
There is no significant correlation between SALES and Quarter also between SALES and RADIO. This is the reason why he slopes for these two variables are problematic here.
SALES
QTR
TV
RADIO
NEWS
88
1
100
95
87
80
2
99
99
98
96
3
101
103
101
76
4
93
95
91
80
1
95
102
88
73
2
95
94
84
58
3
80
89
74
116
4
116
112
102
104
1
106
110
105
99
2
105
87
97
64
3
90
90
88
126
4
113
101
108
94
1
96
100
89
71
2
98
85
78
111
3
109
99
109
109
4
102
101
108
100
1
100
93
102
127
2
107
108
110
99
3
108
100
95
82
4
95
69
90
67
1
91
95
85
100
2
114
91
103
78
3
93
80
80
115
4
115
85
104
83
1
97
105
83
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