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Running head: ECON 3100
Econ 3100
Student’s Name:
Instructor’s Name:
Institutional Affiliation:
ECON 3100
2
Problem set 6
Statistical investigation:
This exercise draws on the dataset “companies,” available in JMP under “sample data setsBusiness and Demographic” and on the course website. The goal is for you to learn to
incorporate qualitative variables into multiple regression analysis and to interpret the results
appropriately. We will analyze the profits of a set of companies in relationship to those
companies’ sales, number of employees, and industry.
1. Run a regression with profits as the dependent variable, sales and the number of
employees as the independent variables. Call this Model A, and include the
regression output in your problem set.
Coefficientsa
Model
Unstandardized
Standardized
Coefficients
Coefficients
B
(Constant)
1
sales
employees
Std. Error
111.283
78.031
.104
.027
-.007
.004
t
Sig.
Beta
1.426
.165
1.469
3.906
.001
-.611
-1.624
.115
a. Dependent Variable: profits
2. Conduct an F-test at a 5% significance level as to whether there is a useful
relationship between the dependent variable and the independent variables of
Model A.
ANOVAa
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Model
Sum of
df
Mean
Squares
Square
14805831.31
7402915.65
Regression
2
52.768
8
1
F
Residual
4068454.211
Sig.
.000b
9
29
140291.525
18874285.52
Total
31
9
a. Dependent Variable: profits
b. Predictors: (Constant), employees, sales
Fcalculated = 52.768
Fcritical = Fk-1, n-k, s.f
F = 2-1, 32-2,5%
F1,30,5%
Fcritical = 4.17
Inference
Fcalc > Fcritical
52.768 > 4.17
Since the calculated F is greater than the critical F, the null hypothesis which says that the model
is not significant is rejected. The conclusion is that the overall model is statistically significant.
3. What are the r-squared and the adjusted r-squared of Model A? Interpret each of these
values.
Model Summaryb
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ECON 3100
Mode
4
R
R Square
l
1
.886a
.784
Adjusted R
Std. Error of
Square
the Estimate
.770
374.555
a. Predictors: (Constant), employees, sales
b. Dependent Variable: profits
From the output, the r-squared is 0.784 while the adjusted R square is 0.770. The R-squared is
also known as coefficient of determination and it is a measure of goodness of fit. R-square
measures how close the data fits the regression line and it measures the strength of the
relationship between the model and the dependent variable. The higher the r-square, the better
the model fits your data (Darlington & Hayes, 2016). From the above model, the r-squared is
0.784 implying that the model explains 78.4% of the data variation around its mean. The
adjusted r-square on the other hand is computed by dividing the residual mean square error by
the total mean square error after which the result is subtracted from 1. The adjusted r2 explains
the variation when adjusted to the degrees of freedom. It shows the descriptive power of
regression models which take into account the diverse number of predictors. The adjusted r2
accounts for the percentage of variation explained by only the independent variables which
actually affect the dependent variable (Darlington & Hayes, 2016). From the model, the adjusted
r-square is equal to 0.770 implying that the model explains 77% of the variation of data around
the mean when adjusted to the degrees of freedom.
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4. Create a dummy variable that that takes the value 1 if the company is in the computer
industry, 0 if the company is in the pharmaceutical industry.
Model Summaryb
Mode
R
R Square
Adjusted R
Std. Error of
Square
the Estimate
l
.935a
1
.874
.860
291.612
a. Predictors: (Constant), dummy, sales, employees
b. Dependent Variable: profits
5. Run a regression with profits as the dependent variable, sale, the number of employees,
and the dummy variable for “computer industry” as the independent variables. Call this
Model B, and include the regression output in your problem set.
Model B
Coefficientsa
Model
Unstandardized
Standardized
Coefficients
Coefficients
B
(Constant)
sales
Std. Error
400.713
88.951
.100
.021
-.006
-475.169
t
Sig.
Beta
4.505
.000
1.409
4.806
.000
.003
-.541
-1.845
.076
106.671
-.300
-4.455
.000
1
employees
dummy
a. Dependent Variable: profits
6. Adjusted for the number of variables in the model, which model explains the greater
share of variation in profits, Model A or Model B?
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Model A
Model Summaryb
Mode
R
R Square
l
1
.886a
Adjusted R
Std. Error of
Square
the Estimate
.784
.770
374.555
a. Predictors: (Constant), employees, sales
b. Dependent Variable: profits
Model B
Model Summaryb
Mode
R
R Square
l
1
.935a
Adjusted R
Std. Error of
Square
the Estimate
.874
.860
291.612
a. Predictors: (Constant), dummy, sales, employees
b. Dependent Variable: profits
The r-square and adjusted r-square of Model B is higher than that of Model A and hence it the
model that explains better the share of variation in profits.
7. Interpret the coefficient on the dummy variable for computer industry in model B.
Y = a + bx
Profits = Sales ($M) + #employ + Type (computer=1, pharmaceutical=0)
Profits = 400.713 + 0.1Sales ($M) -0.006#Employ- 475.169Type
For the computer industry, value = 1
Profits = 400.713 + 0.1Sales ($M) -0.006#Employ- 475.169(1)
Profits = 400.713 + 0.1Sales ($M) -0.006#Employ- 475.169
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Profits = 400.713 + 0.100Sales ($M) -0.006#Employ- 475.169
Profits = -74.4567 + 0.100Sales ($M) -0.006#Employ
The coefficient on...