A study was undertaken to examine the profits per sales dollars earned by a cons
ID: 3179619 • Letter: A
Question
A study was undertaken to examine the profits per sales dollars earned by a construction company and its relationship to the size of the construction contract (CS, in hundreds of thousands of dollars) and the number of years of experience of the construction supervisor (SE). Data are recorded in the excel file (which is posted on the course website with the tab "Question 1"). a. Consider the model: Model 1: Profit = beta_0 + beta_1 CS + beta_2 SE + u where u is the random error. Obtain the least squares estimate beta_0, beta_1 and beta_2. b. Consider the model: Model 2: Profit = alpha_0 + alpha_1 CS + v where v is the random error. Obtain the least squares estimate alpha_0, and alpha_1. c. Describe when omitted SE from the model, what happen to alpha_1. d. Consider the model: Model 3: SE = delta_0 + delta_1 CS + w where 2 is the random error. Obtain the least squares estimate delta_0, and delta_1. e. Demonstrate that alpha_1 = beta_2 delta_1.Explanation / Answer
Result:
a).
Regression Analysis
R²
0.328
Adjusted R²
0.239
n
18
R
0.573
k
2
Std. Error
1.999
Dep. Var.
Profit
ANOVA table
Source
SS
df
MS
F
p-value
Regression
29.3211
2
14.6605
3.67
.0505
Residual
59.9567
15
3.9971
Total
89.2778
17
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
8.0136
1.4454
5.544
.0001
4.9328
11.0944
CS
-1.3548
0.5530
-2.450
.0271
-2.5336
-0.1760
SE
0.4626
0.4346
1.065
.3039
-0.4636
1.3889
Profit = 8.0136-1.3548CS+0.4626 SE
b).
Regression Analysis
r²
0.278
n
18
r
-0.527
k
1
Std. Error
2.008
Dep. Var.
Profit
ANOVA table
Source
SS
df
MS
F
p-value
Regression
24.7911
1
24.7911
6.15
.0246
Residual
64.4867
16
4.0304
Total
89.2778
17
Regression output
confidence interval
variables
coefficients
std. error
t (df=16)
p-value
95% lower
95% upper
Intercept
8.2475
1.4345
5.749
2.99E-05
5.2065
11.2886
CS
-0.9146
0.3688
-2.480
.0246
-1.6964
-0.1328
Profit = 8.2475-0.9146 CS
c).
The regression coefficient is changed from to -0.9146, increased.
d).
Regression Analysis
r²
0.559
n
18
r
0.748
k
1
Std. Error
1.150
Dep. Var.
SE
ANOVA table
Source
SS
df
MS
F
p-value
Regression
26.8335
1
26.8335
20.28
.0004
Residual
21.1665
16
1.3229
Total
48.0000
17
Regression output
confidence interval
variables
coefficients
std. error
t (df=16)
p-value
95% lower
95% upper
Intercept
0.5057
0.8219
0.615
.5470
-1.2365
2.2480
CS
0.9515
0.2113
4.504
.0004
0.5037
1.3994
SE= 0.5057+0.9515 CS
e).
1+21= -1.3548+0.4626*0.9515 = -0.9146361
=1
Regression Analysis
R²
0.328
Adjusted R²
0.239
n
18
R
0.573
k
2
Std. Error
1.999
Dep. Var.
Profit
ANOVA table
Source
SS
df
MS
F
p-value
Regression
29.3211
2
14.6605
3.67
.0505
Residual
59.9567
15
3.9971
Total
89.2778
17
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
8.0136
1.4454
5.544
.0001
4.9328
11.0944
CS
-1.3548
0.5530
-2.450
.0271
-2.5336
-0.1760
SE
0.4626
0.4346
1.065
.3039
-0.4636
1.3889
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