Multiple regression analysis is widely used in business research in order to for
ID: 3305074 • Letter: M
Question
Multiple regression analysis is widely used in business research in order to forecast and predict purposes. It is also used to determine what independent variables have an influence on dependent variables, such as sales.
Sales can be attributed to quality, customer service, and location. In multiple regression analysis, we can determine which independent variable contributes the most to sales; it could be quality or customer service or location.
Now, consider the following scenario. You have been assigned the task of creating a multiple regression equation of at least three variables that explains Microsoft’s annual sales.
Use a time series of data of at least 10 years. You can search for this data using the Internet.
Before running the regression analysis , predict what sign each variable will be and explain why you made that prediction.
Run three simple linear regressions by considering one independent variable at a time
After running each of the three linear regressions, interpret the regression.
Does the regression fit the data well?
Run a multiple regression using all three independent variables.
Interpret the multiple regression. Does the regression fit the data well?
Does each predictor play a significant role in explaining the significance of the regression?
Are some predictors not useful?
If so, did you consider removing those and rerunning the regression?
Are the predictors related too significantly to one another? What is the coefficient of correlation “r”? Do you think this “r” value suggests a strong correlation among the predictors ( the independent variables?
This is the whole assignment.
What I have so far:
Prediction
Time
X1
X2
X3
1
30
12
94
2
47
10
108
3
25
17
112
4
51
16
178
5
40
5
94
6
51
19
175
7
74
7
170
8
36
12
117
9
59
13
142
10
76
16
211
The regression analysis: Y vs. X1
SE Coef
S= 25.4009 R-Sq= 66.0%R-Sq (adj)= 61.8%
Analysis of Variance
Residual Error
645
Estimated regression equation
Estimate of Y when (x1) = 45:
^y= 45.1+1.94(X1)
Regression Analysis: Y vs. X2
Y=85.2+4.32X2
Predictor
Coef
SE Coef
T
P
Constant
85.22
38.35
2.22
0.057
X2
4.321
2.864
1.51
0.170
S= 38.4374 R-Sq= 22.2% R-Sq (adj)= 12.4%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
1
3363
3363
2.28
0.170
Residual Error
8
11819
1477
Total
9
15183
^y=85.2+4.32(X1)
=85.2+4.32(15)
=150
Regression Analysis: Y vs. X1, X2
Y=-18.4+2.01(X1)+4.74(X2)
Predictor
Coef
SE Coef
T
P
Constant
-18.37
17.97.
-1.02
0.341
X1
2.0102
0.2471
8.13
0.000
X2
4.7378
0.9484
5.00
0.002
S=12.7096 R-Sq= 92.6% R-Sq (adj)= 90.4%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
2
14052.2
7026.1
43.50
0.000
Residual Error
7
1130.7
161.5
Total
9
15182.9
Source
DF
Seq. SS
X1
1
10021.2
X2
1
4030.9
Estimated regression equation:
^Y= -18.4+2.01(X1) + 4.74(X2)
Y= If (X1)=45, (X2)=15
^y= -18.4+2.01(X1)+4.74(X2)
=-18.4+2.01(45)+4.74(15)
=143.15
Linear regression 1
Microsoft annual sales
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
51.12
60.42
58.44
62.48
69.94
73.72
77.85
86.83
93.58
85.32
Time
X1
X2
X3
1
30
12
94
2
47
10
108
3
25
17
112
4
51
16
178
5
40
5
94
6
51
19
175
7
74
7
170
8
36
12
117
9
59
13
142
10
76
16
211
Explanation / Answer
Interpret the multiple regression. Does the regression fit the data well?
yes , the r sqaure value for multiple regression is R-Sq= 92.6%. Hence the model is able to capture and explain 92.6% variation in the data
Does each predictor play a significant role in explaining the significance of the regression?
from the below table
Predictor
Coef
SE Coef
T
P
Constant
-18.37
17.97.
-1.02
0.341
X1
2.0102
0.2471
8.13
0.000
X2
4.7378
0.9484
5.00
0.002
we see that the p value for x1 and x2 is less than 0.05 , hence at an alpha of 0.05 we can conclude that noth x1 and x2 variables contribute significantly in explaining the variation of the data
Are some predictors not useful?
No , for the muliple regression analysis both x1 and x2 are significant
If so, did you consider removing those and rerunning the regression?
if x3 is also used for the regression analysis , then we must recheck the p values of all x1,x2 and x3 variable. if any variable has a p value greater than 0.05 , then we can remove that variable from the regression analysis
Are the predictors related too significantly to one another? What is the coefficient of correlation “r”? Do you think this “r” value suggests a strong correlation among the predictors ( the independent variables?
The coefficient of correlation is
sqrt(0.926) = 0.962
we must check the correlation between all variables to see if the variables have high correlation. also , another way is if none of the variables are statistically signficant but the model as a whole is sigificant(significant f is less than 0.05) then the model has problem of multicollinearity
Predictor
Coef
SE Coef
T
P
Constant
-18.37
17.97.
-1.02
0.341
X1
2.0102
0.2471
8.13
0.000
X2
4.7378
0.9484
5.00
0.002
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.