Question

You want to construct a multiple linear regression model. The dependent variable is Y and independent variables are x1 and x2. The samples and STATA outputs are provided:

Y | X1 | X2 |

3 | 2 | 1 |

4 | 1 | 2 |

6 | 3 | 3 |

6 | 3 | 4 |

7 | 4 |
5 |

STATA

Y |
Coef. |
Std. Err. |
t |
P> abs. value (t) |
95% confidence interval |

X1 | 0.25 | 0.4677072 | 0.53 | 0.646 | -1.762382 , 2.262382 |

X2 | 0.85 | 0.3372684 | 2.52 | 0.128 | -.601149 , 2.301149 |

_cons | 2 | 0.7245688 | 2.76 | 0.110 | -1.117568 , 5.117568 |

A) Calculate the SST, SSE and SSR

B) Draw the ANOVA table below

C) Calculate S^{2} , R^{2} , and adjusted
R^{2}

Please show steps, and thanks!

Answer #1

You want to construct a multiple linear regression model. The
dependent variable is Y and independent variables are x1 and x2.
The samples and STATA outputs are provided:
Y
X1
X2
3
2
1
4
1
2
6
3
3
6
3
4
7
4
5
STATA
Y
Coef.
Std. Err.
t
P> abs. value (t)
95% confidence interval
X1
0.25
0.4677072
0.53
0.646
-1.762382 , 2.262382
X2
0.85
0.3372684
2.52
0.128
-.601149 , 2.301149
_cons
2
0.7245688
2.76
0.110...

You want to construct a multiple linear regression model. The
dependent variable is Y and independent variables are x1 and x2.
The samples and STATA outputs are provided:
How would you make an ANOVA from the following information?
Y
X1
X2
3
2
1
4
1
2
6
3
3
6
3
4
7
4
5
STATA
Y
Coef.
Std. Err.
t
P> abs. value (t)
95% confidence interval
X1
0.25
0.4677072
0.53
0.646
-1.762382 , 2.262382
X2
0.85
0.3372684...

8. Consider the following data for a dependent variable
y and two independent variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
(a) Develop an estimated regression equation relating y
to x1. (Round your numerical values to one decimal
place.)
ŷ = ______
Predict y if x1 = 51. (Round
your answer...

The following information regarding a dependent variable (Y) and
an independent variable (X) is provided.
Y
X
4
2
3
1
4
4
6
3
8
5
SSE = 6
SST = 16
Refer to Exhibit 12-4. The least squares estimate of the slope
is
Question 7 options:
1
2
3
4

Consider the following data for a dependent variable y
and two independent variables, x1and
x2; for these data SST = 15,309.6, and SSR =
14,429.8.
x 1
x 2
y
30
12
94
47
10
109
25
17
113
51
17
179
41
5
94
51
19
176
74
7
170
36
13
118
59
13
143
76
17
212
Round your answers to three decimal places.
a. Compute R2.
b. Compute
Ra2.

A multiple linear regression model based on a sample of 17 weeks
is developed to predict standby hours based on the total staff
present and remote hours. The SSR is 20,905.02 and the SSE is
25,434.29. (use 0.05 level of significance)
H0: B1 = B2 = 0
H1: At least one Bj does not equal 0, j = 1, 2
1. Calculate the test statistic.
Fstat= _____
2. Find the p-value.
p-value= _____
3. Compute the coefficient of multiple determination,...

The estimated
regression equation for a model involving two independent variables
and 55 observations is:
y-hat = 55.17 +
1.1X1 - 0.153X2
Other statistics produced for analysis
include:
SSR = 12370.8
SST = 35963.0
Sb1 = 0.33
Sb2 = 0.20
Interpret b1 and b2 in this estimated regression equation
b. Predict y when X1 = 55 and X2 =
70.
Compute R-square and Adjusted R-Square.
e. Compute MSR and MSE.
f. Compute F and use it to test
whether the...

1）The following information regarding a dependent variable y and
an independent variable x is provided.
Σx = 90
Σy = 340
n = 4
SSR = 101
Additionally, the SSE is equal to 1,872. Find the standard error
of the estimate.
A 7.1063
B 21.6333
C 30.5941
D 44.4185
2）
Consider the data.
Compute the standard error of the estimate.
xi 3 12 6 20 14
yi 60 40 45 5 15

Exhibit 6
The following information regarding a dependent variable (Y) and
an independent variable (X) is provided.
Y X
4 2
6 3
8 4
8 5
11 6
Also given are SSE=1.6 and SST=27.2.
a. Refer to Exhibit 6. What is the least squares estimated
regression equation?
A. Yhat = 1 + 1.6X
B. Yhat = 2 + 3.2X
C. Yhat = 1.6 + 27.2X
D. Yhat = 27.2 + 4.6X
b. Refer to Exhibit 6. What is the...

Multiple linear regression results:
Dependent Variable: Cost
Independent Variable(s): Summated Rating
Cost = -43.111788 + 1.468875 Summated Rating
Parameter estimates:
Parameter
Estimate
Std. Err.
Alternative
DF
T-Stat
P-value
Intercept
-43.111788
10.56402
≠ 0
98
-4.0810021
<0.0001
Summated Rating
1.468875
0.17012937
≠ 0
98
8.633871
<0.0001
Analysis of variance table for multiple regression model:
Source
DF
SS
MS
F-stat
P-value
Model
1
8126.7714
8126.7714
74.543729
<0.0001
Error
98
10683.979
109.02019
Total
99
18810.75
Summary of fit:
Root MSE: 10.441273
R-squared: 0.432...

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