Question

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 of sig.

b. Calculate the coefficient of determination

c. What is the estimated regression equation?

d. Use the p-value approach to perform a t test for the
significance of the linear relationship between Price and Rating at
the 0.05 level of significance.

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...

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...

Shown below is a portion of an Excel output for regression
analysis relating Y (dependent variable) and X (independent
variable).
ANOVA
df
SS
Regression
1
39947.80
Residual (Error)
10
8280.81
Total
11
48228.61
Coefficients
Standard Error
t Stat
P-value
Intercept
69.190
26.934
2.569
0.02795
X
2.441
0.351
6.946
0.00004
1. What is the estimated regression equation
that relates Y to X?
2. Is the regression relationship significant?
Use the p-value approach and alpha = 0.05 to answer this
question.
3. What is the...

The following regression output was obtained from a study of
architectural firms. The dependent variable is the total amount of
fees in millions of dollars.
Predictor
Coeff
SE
Coeff
t
p-value
Constant
8.366
3.002
2.787
0.010
X1
0.225
0.301
0.748
0.000
X2
–1.216
0.538
–2..260
0.028
X3
-0.070
0.377
–0.186
0.114
X4
0.552
0.322
1.714
0.001
X5
-0.049
0.028
–1.750
0.112
Analysis of Variance
Source
DF
SS
MS
F
p-value
Regression
5
2197.68
439.5
9.68
0.000
Residual Error
59
2679.56...

The following regression output was obtained from a study of
architectural firms. The dependent variable is the total amount of
fees in millions of dollars.
Predictor
Coefficient
SE Coefficient
t
p-value
Constant
9.387
3.069
3.059
0.010
x1
0.232
0.204
1.137
0.000
x2
−
1.214
0.584
−
2.079
0.028
x3
−
0.273
0.424
−
0.644
0.114
x4
0.642
0.362
1.773
0.001
x5
−
0.060
0.028
−
2.143
0.112
Analysis of Variance
Source
DF
SS
MS
F
p-value
Regression
5
2,364.50
472.9...

Shown below is a portion of an Excel
output for regression analysis relating Y (dependent variable) and
X (independent variable).
ANOVA
df
SS
Regression
1
3348.312
Residual
8
9529.811
Total
9
12878.123
Coefficients
Standard Error
t Stat
P-value
Intercept
247.56
83.280
1.689
0.030
X
148.62
38.312
1.283
0.075
1. What is the estimated regression equation that relates y to x?
(2 Points)
2. Is the regression relationship significant? Use a p-value and
alpha = 0.05. (2 Points)
3. What is...

The following table is the output of simple linear regression
analysis. Note that in the lower right hand corner of the output we
give (in parentheses) the number of observations, n, used
to perform the regression analysis and the t statistic for
testing H0: β1 = 0 versus
Ha: β1 ≠ 0.
ANOVA
df
SS
MS
F
Significance F
Regression
1
61,091.6455
61,091.6455
.69
.4259
Residual
10
886,599.2711
88,659.9271
Total
11
947,690.9167
(n = 12;...

Use regression analysis to examine the variation in a dependent
variable. Use 0.05 level of significance unless other
stated.
When doing various tests (fit, significance) report the
relevant values of the parameters (test stats, R square)
Make sure to write out your hypotheses and rejection rules for
significance tests. If p-values are greater than 0
report the level at which your test is significant.
Conclusions are to be in terms of the problems; pretend the
reader has no idea about you were...

Study the following Minitab output from a regression analysis to
predict y from x. a. What is the equation of the regression model?
b. What is the meaning of the coefficient of x? c. What is the
result of the test of the slope of the regression model? Let α =
.10.Why is the t ratio negative? d. Comment on r2 and the standard
error of the estimate. e. Comment on the relationship of the F
value to the t...

] A partial computer output from a regression analysis using
Excel’s Regression tool follows. Regression Statistics Multiple R
(1) R Square 0.923 Adjusted R Square (2) Standard Error 3.35
Observations ANOVA df SS MS F Significance F Regression (3) 1612
(7) (9) Residual 12 (5) (8) Total (4) (6) Coefficients Standard
Error t Stat P-value Intercept 8.103 2.667 x1 7.602 2.105 (10) x2
3.111 0.613 (11)

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