Question

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

R-squared (adjusted): 0.4262

Predicted values stored in new column: Pred. Value

9. Using your data file **Restaurants** , find:
**Summated Rating = Independent Variable; Cost = Dependent
Variable**

a. What is an appropriate null hypothesis for this simple linear
regression? b. What is the test statistic (F) for the
regression? c. What is the value for *Significance F* for
the regression d. What is your conclusion concerning the null
hypothesis? Reject / Not Reject? e. What is the value of the r
square? f. Interpret R Square (what does it mean)? g. What is the
value of the slope? h. What is the value of the y intercept?

Answer #1

The following output was obtained from a regression analysis of
the dependent variable Rating and an independent variable Price.
(10 points)
ANOVA
df
SS
MS
F
Regression
1
372.707
372.707
42.927
Residual
15
130.234
8.682
Total
16
502.941
Coefficients
Standard Error
t Stat
P-value
Intercept
45.623
3.630
12.569
0.000
Price
0.107
0.016
6.552
0.000
Use the critical value approach to perform an F test for the
significance of the linear relationship between Rating and Price at
the 0.05 level of...

1. The following output was obtained from a regression
analysis of the dependent variable Rating and an independent
variable
Price.
Anova
df SS MS f
Regression 1 301.701 301.701 32.94
Residual 15 128.221 9.1586
Total 16 429.922
Coefficients Standard Error T Stat P value
Intercept 45.623 3.630 12.569 0.000
Price .107 0.016 6.552 0.002
a. Use the critical value approach to perform an F test for the
significance of the linear relationship between Rating and Price at
the 0.05 level...

SUMMARY OUTPUT
Dependent
X variable:
all other variables
Regression Statistics
Independent
Y variable:
oil usage
Multiple R
0.885464
R
Square
0.784046
variation
Adjusted R Square
0.76605
Standard Error
85.4675
Observations
40
ANOVA
df
SS
MS
F
Significance F
Regression
3
954738.9
318246.3089
43.56737
4.55E-12
Residual
36
262969
7304.693706
Total
39
1217708
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-218.31
63.95851
-3.413304572
0.001602
-348.024
-88.596
-348.024
-88.596
Degree Days
0.275079
0.036333
7.571119093
5.94E-09...

Consider the following results of a multiple regression model of
dollar price of unleaded gas (dependent variable) and a set of
independent variables: price of crude oil, value of S&P500,
price U.S. Dollars against Euros, personal disposal income (in
million of dollars) :
Coefficient
t-statistics
Intercept
0.5871
68.90
Crude Oil
0.0651
32.89
S&P 500
-0.0020
18.09
Price of $
-0.0415
14.20
PDI
0.0001
17.32
R-Square = 97%
What will be forecasted price of unleaded gas if the value of
independent...

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...

True or False: Please specify your reasons.
(i) If an independent variable in a multiple linear regression
model is an exact linear combination of other independent
variables, we can still calculate the least square estimators of
the intercept.
(ii) For the multiple linear regression y = β0 + β1x + β2x 2 +
u, β1 can be interpreted as the effect of one unit increase in x on
y.
(iii) In the multiple linear regression with an intercept, (the
sum...

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:
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. For the following multiple regression which was
conducted to attempt to predict the variable based on the
independent variables shown, answer the following
questions.
Regression Statistics
Multiple R
0.890579188
R Square
0.793131289
Adjusted R Square
0.7379663
Standard Error
30.28395534
Observations
20
ANOVA
df
SS
MS
F
Regression
4
52743.23074
13185.81
14.37743932
Residual
15
13756.76926
917.1179509
Total
19
66500
Coefficients
Standard Error
t Stat
P-value
Intercept
73.33291
62.25276
1.17799
0.25715
X1
-0.13882
0.05353
-2.59326
0.02037
X2
3.73984
0.95568
3.91328
0.00138...

19. In a linear regression model if the mean of the
independent variable data is 10, the mean of the
dependent
variable data is 75 and the
slope is 5, the intercept is
a. 25
b. 7
c. -25
d. 13
20. In a linear regression model if the mean of the
independent variable data is 10, the mean of the
dependent
variable data is 75 and the
slope is 5, if xequals 15, the forecast,
y, is
a. 75...

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