Question
In: Statistics and Probability
The following portion of regression results was obtained when estimating a simple linear regression model. df...
- The following portion of regression results was obtained when estimating a simple linear regression model.
|
df |
SS |
MS |
F |
|
|
Regression |
1 |
725.56 |
725.56 |
751.68 |
|
Residual |
23 |
22.20 |
B |
|
|
Total |
24 |
A |
||
|
Coefficients |
Standard Error |
t-stat |
p-value |
|
|
Intercept |
80.30 |
2.08 |
38.68 |
1.95E-22 |
|
x |
−0.28 |
0.01 |
-27.42 |
4.54E-19 |
- What is the sample regression equation?
- Interpret the slope coefficient for x1.
- Find the predicted value for y if x1 equals 200.
- Fill in the missing values A and B in the ANOVA table.
- Calculate the standard error of the estimate.
f. Calculate R2.
Solutions
orchestra answered 1 year agoRelated Solutions
he following ANOVA table was obtained when estimating a multiple linear regression model. ANOVA df SS...
he following ANOVA table was obtained when estimating a multiple
linear regression model.
ANOVA
df
SS
MS
F
Significance F
Regression
2
22,009.81
11,004.905
0.0225
Residual
17
39,118.31
2,301.077
Total
19
61,128.12
a-1. How many explanatory variables were
specified in the model?
a-2. How many observations were used?
b. Choose the hypotheses to determine whether
the explanatory variables are jointly significant.
H0: β1 =
β2 = 0; HA: At
least one βj > 0
H0: β1 =
β2 = 0;...
When estimating a multiple linear regression model based on 30 observations, the following results were obtained....
When estimating a multiple linear regression model based on 30
observations, the following results were obtained. [You may
find it useful to reference the t table.]
Coefficients
Standard Error
t Stat
p-value
Intercept
153.08
122.34
1.251
0.222
x1
12.64
2.95
4.285
0.000
x2
2.01
2.46
0.817
0.421
a-1. Choose the hypotheses to determine whether
x1 and y are linearly
related.
H0: β0 ≤ 0;
HA: β0 > 0
H0: β1 ≤ 0;
HA: β1 > 0
H0: β0 = 0;...
The following ANOVA table was obtained when estimating a multiple regression model. ANOVA df SS MS...
The following ANOVA table was
obtained when estimating a multiple regression model.
ANOVA
df
SS
MS
F
Significance F
Regression
2
188,246.80
94,123.40
35.2
9.04E-07
Residual
17
45,457.32
2,673.96
Total
19
233,704.10
a.
Calculate the standard error of
the estimate. (Round your answer to 2 decimal
places.)
se
b-1.
Calculate the coefficient of
determination. (Round your answer to 4 decimal
places.)
Coefficient of
determination
b-2.
Interpret the coefficient of
determination.
The...
Following is a simple linear regression model: yi = a+ bxi +ei The following results were...
Following is a simple linear regression model:
yi = a+
bxi +ei
The following results were obtained from some statistical
software.
R2 = 0.523
syx(regression standard error) = 3.028
n (total observations) = 41
Significance level = 0.05 = 5%
Variable
Parameter Estimate
Std. Err. of Parameter Est.
Interecpt
0.519
0.132
Slope of X
-0.707
0.239
Note: For all the calculated numbers, keep three
decimals.
6.
A 95% confidence interval for the slope b in the simple
linear regression model...
When we estimate a linear multiple regression model (including a linear simple regression model), it appears...
When we estimate a linear multiple regression model (including a
linear simple regression model), it appears that the calculation of
the coefficient of determination, R2, for this model can be
accomplished by using the squared sample correlation coefficient
between the original values and the predicted values of the
dependent variable of this model.
Is this statement true? If yes, why? If not, why not? Please use
either matrix algebra or algebra to support your reasoning.
Simple Linear Regression: Suppose a simple linear regression analysis provides the following results: b0 = 6.000, b1...
Simple Linear Regression: Suppose a simple
linear regression analysis provides the following
results:
b0 = 6.000, b1 =
3.000, sb0 =
0.750,
sb1 =
0.500, se = 1.364
and n = 24. Use this information to answer the following
questions.
(a) State the model equation.
ŷ = β0 + β1x
ŷ = β0 + β1x +
β2sb1
ŷ = β0 + β1x1 +
β2x2
ŷ = β0 +
β1sb1
ŷ = β0 +
β1sb1
x̂ = β0 +
β1sb1
x̂ = β0 +...
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Questions:
Interpret each coefficient.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Question:
1.
A. Write the fitted regression equation.
B. Write the estimated intercepts and slopes, associated with
their corresponding standard errors.
C. Interpret each coefficient.
Which of the following is the complete definition of the simple linear regression model?
Which of the following is the complete definition of the simple
linear regression model?
Exercise 15-6 Algo When estimating a multiple linear regression model based on 30 observations, the following...
Exercise 15-6 Algo
When estimating a multiple linear regression model based on 30
observations, the following results were obtained. [You may
find it useful to reference the t table.]
Coefficients
Standard Error
t Stat
p-value
Intercept
153.35
126.57
1.212
0.236
x1
11.10
2.62
4.237
0.000
x2
2.36
2.06
1.146
0.261
a-1. Choose the hypotheses to determine whether
x1 and y are linearly related.
H0: β1 = 0;
HA: β1 ≠ 0
H0: β0 = 0;
HA: β0 ≠ 0
H0:...
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