The following output was obtained from a multiple regression analysis. Analysis of variance SOURCE DF SS MS Regression 5 100 20 Residual Error 20 40 2 Total 25 140 Predictor Coefficient SE Coefficient t Constant 3.00 1.50 2.00 x1 4.00 3.00 1.33 x2 3.00 0.20 15.00 x3 0.20 0.05 4.00 x4 −2.50 1.00 −2.50 x5 3.00 4.00 0.75 a. What is the sample size? b. Compute the value of R2. (Round your answer to 4 decimal places.) c. Compute the multiple standard error of estimate. (Round your answer to 4 decimal places.) Conduct a global test of hypothesis H0: β1 = β2 = β3 = β4 = β5 = 0; H1: Not all β's are 0 at the 0.05 significance level. d-1. State the decision rule. (Round your answer to 2 decimal places.) Reject H0 if F> d-2. What is the computed value of F? (Round your answer to 1 decimal place.) Value of F d-3. Determine whether any of the regression coefficients are significant. ----------------Reject H0 Atleast One regression Coefficient is---------------- Accept Zero Reject Not Zero e-1. What is the decision rule for individual regression coefficients? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) H0 is Rejected in each case if t<--------------or t>--------------- e-2. Which variables would you consider eliminating? x1 and x5 x2 and x3 x3 and x4 x1 and x2
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The following output was obtained from a multiple
| Analysis of variance | ||||||
| SOURCE | DF | SS | MS | |||
| Regression | 5 | 100 | 20 | |||
| Residual Error | 20 | 40 | 2 | |||
| Total | 25 | 140 | ||||
| Predictor | Coefficient | SE Coefficient | t | |||
| Constant | 3.00 | 1.50 | 2.00 | |||
| x1 | 4.00 | 3.00 | 1.33 | |||
| x2 | 3.00 | 0.20 | 15.00 | |||
| x3 | 0.20 | 0.05 | 4.00 | |||
| x4 | −2.50 | 1.00 | −2.50 | |||
| x5 | 3.00 | 4.00 | 0.75 | |||
a. What is the
b. Compute the value of R2. (Round your answer to 4 decimal places.)
c. Compute the multiple standard error of estimate. (Round your answer to 4 decimal places.)
Conduct a global test of hypothesis H0: β1 = β2 = β3 = β4 = β5 = 0; H1: Not all β's are 0 at the 0.05 significance level.
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d-1. State the decision rule. (Round your answer to 2 decimal places.)
Reject H0 if F>
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d-2. What is the computed value of F? (Round your answer to 1 decimal place.)
Value of F
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d-3. Determine whether any of the regression coefficients are significant.
----------------Reject H0 Atleast One regression Coefficient is----------------
Accept Zero
Reject Not Zero
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e-1. What is the decision rule for individual regression coefficients? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
H0 is Rejected in each case if t<--------------or t>---------------
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e-2. Which variables would you consider eliminating?
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x1 and x5
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x2 and x3
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x3 and x4
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x1 and x2
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