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}

I really appreciate the help!

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 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...

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...

1. In a multiple
regression model, the following coefficients were obtained:
b0 = -10 b1
= 4.5 b2 = -6.0
a. Write the
equation of the estimated multiple regression model. (3 pts)
b Suppose a
sample of 25 observations produces this result, SSE = 480. What is
the estimated standard error of the estimate? (5 pts)
2. Consider the
following estimated sample regression equation:
Y = 12 + 6X1 -- 3 X2
Determine which of the following
statements are true,...

Part C: Regression and Correlation Analysis
Use the dependent variable (labeled Y) and the independent
variables (labeled X1, X2, and X3) in the data file. Use Excel to
perform the regression and correlation analysis to answer the
following.
Generate a scatterplot for the specified dependent variable (Y)
and the X1 independent variable, including the graph of the "best
fit" line. Interpret.
Determine the equation of the "best fit" line, which describes
the relationship between the dependent variable and the selected...

1.A real estate analyst has developed a multiple regression
line, y = 60 + 0.068 x1 – 2.5
x2, to predict y = the market
price of a home (in $1,000s), using two independent variables,
x1 = the total number of square feet of living
space, and x2 = the age of the house in years.
With this regression model, the predicted price of a 10-year old
home with 2,500 square feet of living area is __________.
$205.00
$255,000.00
$200,000.00...

Use the dependent variable (labeled Y) and the independent
variables (labeled X1, X2, and X3) in the data file. Use Excel to
perform the regression and correlation analysis to answer the
following.
Generate a scatterplot for the specified dependent variable (Y)
and the X1 independent variable, including the graph of the "best
fit" line. Interpret.
Determine the equation of the "best fit" line, which describes
the relationship between the dependent variable and the selected
independent variable.
Determine the coefficient of...

Given here are data for a dependent variable and four potential
predictors.
y
x1
x2
x3
x4
x5
96
8
60
2.4
48
51
73
6
64
2.1
42
43
108
2
76
1.8
34
20
124
5
74
2.2
11
14
82
6
50
1.5
61
29
89
9
57
1.6
53
22
76
1
72
2
72
38
109
3
74
2.8
36
40
123
2
99
2.6
17
50
125
6
81
2.5
48
55
101
2...

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