Question
In: Statistics and Probability
Below you are given a partial computer output from a multiple regression analysis based on a...
Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error Constant 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 4853 2426.5 Error 485.3 Carry out the test of significance for the variable x1 at the 1% level. The null hypothesis should be options: be tested for β₃ instead. be rejected. be revised to test using F statistic. not be rejected.
Solutions
Expert Solution
For F-test:
Hypothesis:
The p-value for the F-test is 0.000 and less than 0.01 level of significance. Hence, we can conclude that at least one predictor has a significant effect on the model.
orchestra answered 2 years agoRelated Solutions
Below you are given a partial computer output based on a sample of 8 observations relating...
Below you are given a partial computer output based on a sample
of 8 observations relating an independent variable ( x)
and a dependent variable ( y).
Coefficient
Standard Error
Intercept
13.251
10.77
x
0.803
0.385
ANOVA
SS
Regression
Error (Residual)
41.674
Total
71.875
a.
Develop the estimated regression equation.
b.
At α = .05, test for the significance of the
slope.
c.
At α = .05, perform an F test.
d.
Determine the coefficient of determination.
Exhibit 15-6 Below you are given a partial computer output based on a sample of 16...
Exhibit 15-6
Below you are given a partial computer output based on a sample of
16 observations.
Coefficient
Standard Error
Constant
12.924
4.425
X1
-3.682
2.630
X2
45.216
12.560
Analysis of Variance
Source of
Variation
Degrees
of Freedom
Sum of
Squares
Mean
Square
F
Regression
4,853
2,426.5
Error
485.3
Refer to Exhibit 15-6. The F value obtained from the table used to
test if there is a relationship among the variables at the 5% level
equals
Group of answer choices...
You are given the following output for a multiple regression based on a sample of size...
You are given the following output for a multiple regression
based on a sample of size n = 10
Predictions
Coefficients
Standard Error
Constant
-0.58762
x1
b1=1.510
0.351
x2
b2=-0.245
0.157
x3
b3=1.823
0.836
SSR=17.56; SSE=8.56
(a) Calculate a 90% confidence interval for β1. Provide a clear
interpretation of the interval.
(b) Which predictor variable(s) – x1, x2, x3 – should be kept in
the regression model and why, if testing at a 5% level of
significance? (use two-sided tests)...
Shown below is a partial Excel output from a regression analysis. ANOVA df SS MS F...
Shown below is a partial Excel output from a regression
analysis.
ANOVA
df
SS
MS
F
Regression
60
Residual
Total
19
140
Coefficients
Standard Error
Intercept
10.00
2.00
x1
-2.00
1.50
x2
6.00
2.00
x3
-4.00
1.00
a.
Use the above results and write the regression equation. [4
Marks]
b.
Compute the coefficient of determination and fully interpret its
meaning. [4 Marks]
c.
Is the regression model significant? Perform the test at let α =
0.05. [4 Marks]
d.
At...
Shown below is a partial Excel output from a regression analysis. ANOVA df SS MS F...
Shown below is a partial Excel output from a regression
analysis.
ANOVA
df
SS
MS
F
Regression
60
Residual
Total
19
140
Coefficients
Standard Error
Intercept
10.00
2.00
x1
-2.00
1.50
x2
6.00
2.00
x3
-4.00
1.00
a.
Use the above results and write the regression equation. [4
Marks]
b.
Compute the coefficient of determination and fully interpret its
meaning. [4 Marks]
c.
Is the regression model significant? Perform the test at let α =
0.05. [4 Marks]
d.
At...
Shown below is a portion of the computer output for a regression analysis relating sales (Y...
Shown below is a portion of the computer output for a
regression analysis relating sales (Y in millions of dollars) and
advertising expenditure (X in thousands of dollars).
Predictor
Coefficient
Standard Error
Constant
4.00
0.800
X
-0.12
0.045
Analysis
of Variance
SOURCE
DF
SS
Regression
1
1,400
Error
18
3,600
Please answer the following questions with showing all the steps
needed.
a. (8’) What has been the
sample size for the above? Please explain how you obtain the answer
using the...
Shown below is a portion of a computer output for a regression analysis relating Y (demand)...
Shown below is a portion of a computer output for a regression
analysis relating Y (demand) and X (unit price). ANOVA df SS
Regression 1 Error 3132.661 Total 47 8181.479 Coefficients Standard
Error Intercept 80.390 3.102 X -2.137 0.248 (a) Compute the
coefficient of determination and fully interpret its meaning. Be
very specific. (b) Find the standard error for b1 (Sb1). (c)
Perform a t test and determine whether or not demand and unit price
are related. Let =...
Below is a partial computer output based on a sample of 40 observations. Coefficient Standard Error...
Below is a partial computer output based on a sample of 40
observations.
Coefficient
Standard Error
Constant
51.696
17.7
X1
-14.728
10.52
X2
180.864
50.24
Analysis of Variance
Source of
Variation
Degrees
of Freedom
Sum of
Squares
Mean
Square
F
Regression
19.412
9.706
Error
1,941.2
Required:
1. Use the output shown above and write the estimated regression
equation.
2. Interpret the meaning of the coefficient of X1 and
X2.
3. Compute the test statistic required to know whether the
parameter...
Given the following regression analysis output.
Given the following regression analysis output. a. What is the sample size?b. How many independent variables are in the study?c. Determine the coefficient of determination.d. Conduct a global test of hypothesis. Can you conclude at least one of the independent variables does not equal zero? Use the .01 significance level.e. Conduct an individual test of hypothesis on each of the independent variables. Would you consider dropping any of the independent variables? If so, which variable or variables would you drop?...
The R output below gives the summary of the multiple regression model for birth weight based...
The R output below gives the summary of the multiple regression
model for birth weight based on both gestation length and smoking
status:
lm(formula = Weight ~ Weeks + SmokingStatus, data = births)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1724.42 558.84 -3.086 0.00265 **
Weeks 130.05 14.52 8.957 2.39e-14 ***
SmokingStatusSmoker -294.40 135.78 -2.168 0.03260 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’
1
Residual standard error: 484.6 on 97 degrees...
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