Question
In: Statistics and Probability
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) [If you want, you can provide your answers in a table with 4 rows. In the 1st row, you can set up 6 columns with the headings: Null Hypothesis; For Which Variable; t-Statistic; Critical t-value; Decision; Keep Variable in Equation?. In the other rows, you show your work for variable x1, x2 and x3]
(c) What is the value of the adjusted-R 2 ? Do you think the regression equation fits the data very well?
Solutions
orchestra answered 2 years agoRelated Solutions
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....
Discuss, sample size, measurement scale and multiple regression and their importance in research
Discuss, sample size, measurement scale and multiple regression and
their importance in research
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 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.
1. Following R output is from fitting multiple regression of House price (Y) in thousand based...
1.
Following R output is from fitting multiple regression of House
price (Y) in thousand based on Finish Area(X1), Age(X2) and
Bedroom(X3).
Coefficients:
Estimate Std. Error t value
Pr(>|t|)
(Intercept) 190.11 2.587 73.48 0.00866
**
X1 2.30 0.010 228.00 0.00279 **
X2 -2.46 0.064 -38.03 0 .01674 *
X3 36.67 0.359 101.96 0.00624 **
-----------------------------
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
Residual standard error: 0.9204 on 1 degrees of
freedom
Multiple R-squared:...
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...
The final part of the multiple regression output is the coefficients table that represents the following:...
The final part of the multiple regression output is the
coefficients table that represents the following:
The unstandardized regression coefficient (B).
The standardized regression coefficient (beta or
β).
t and p values.
All the above.
Three correlation coefficients are displayed in the
coefficients table. They include the following:
The zero order correlation coefficient.
The partial correlation coefficient.
The part correlation coefficient.
All of the above.
If the value for tolerance is acceptable, one should proceed
with interpreting the:
Model summary....
Suppose for a multiple regression on just 5 observations you are given the following portion of...
Suppose for a multiple regression on just 5 observations you are
given the following portion of an excel regression output:
RESIDUAL OUTPUT
Observation
Predicted y(hat)
Residuals
1
73.61
0.39
2
93.03
-1.03
3
58.97
-0.97
4
85.21
-0.21
5
78.18
1.82
Test the model for autocorrelation at a 10% level of
significance.
Test the model for heteroskedasticity using a level of
significance of 5%
Suppose for a multiple regression on just 5 observations you are given the following portion of...
Suppose for a multiple regression on just 5 observations you are
given the following portion of an excel regression output:
RESIDUAL OUTPUT
observations
Predicted y(hat)
Residuals
1
73.61
0.39
2
93.03
-1.03
3
58.97
-0.97
4
85.21
-0.21
5
78.18
1.82
Test the model for autocorrelation at a 10% level of
significance.
Test the model for heteroskedasticity using a level of
significance of 5%
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