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Testing Hypotheses About Regression Coefficients If the
Chapter 10, Problem 17BB(choose chapter or problem)
Testing Hypotheses About Regression Coefficients If the coefficient \(\beta\ 1\) has a nonzero value, then it is helpful in predicting the value of the response variable. If \(\beta\ 1=0\), it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that \(\beta\ 1=0\) use the test statistic \(\mathrm {t=(b\ 1-0)/\ s\ b\ 1}\). Critical values or P-values can be found using the t distribution with \(\mathrm {n-(k+1)}\) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error s b 1 is often provided by software. For example, the Minitab display in Example 1 shows that \(\mathrm {s\ b\ 1=0.1289}\) (found in the column with the heading of SE Coeff and the row corresponding to the first predictor variable of the height of the mother). Use the sample data in Table 10-4 and the Minitab display in Example 1 to test the claim that \(\mathrm {\beta\ 1=0}\). Also test the claim that \(\mathrm {\beta\ 2=0}\). What do the results imply about the regression equation?
Equation Transcription:
Text Transcription:
beta 1
beta 1=0
beta 1=0
t=(b 1-0) / s b 1
n-(k+1)
s b 1=0.1289
beta 1=0
beta 2=0
Questions & Answers
QUESTION:
Testing Hypotheses About Regression Coefficients If the coefficient \(\beta\ 1\) has a nonzero value, then it is helpful in predicting the value of the response variable. If \(\beta\ 1=0\), it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that \(\beta\ 1=0\) use the test statistic \(\mathrm {t=(b\ 1-0)/\ s\ b\ 1}\). Critical values or P-values can be found using the t distribution with \(\mathrm {n-(k+1)}\) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error s b 1 is often provided by software. For example, the Minitab display in Example 1 shows that \(\mathrm {s\ b\ 1=0.1289}\) (found in the column with the heading of SE Coeff and the row corresponding to the first predictor variable of the height of the mother). Use the sample data in Table 10-4 and the Minitab display in Example 1 to test the claim that \(\mathrm {\beta\ 1=0}\). Also test the claim that \(\mathrm {\beta\ 2=0}\). What do the results imply about the regression equation?
Equation Transcription:
Text Transcription:
beta 1
beta 1=0
beta 1=0
t=(b 1-0) / s b 1
n-(k+1)
s b 1=0.1289
beta 1=0
beta 2=0
ANSWER:
Problem 17 BB
Answer:
Step1 of 4:
We have If the coefficientβ1has a nonzero value, then it is helpful in predicting the value of the response variable. If /3j = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that β1= 0 use the test statistics = (b1−0)/sb1.Critical values or P-values can be found using the t distribution with n − (k +1) degrees of freedom, where k is the number of predictor(x)variables and n is the number of observations in the sample. The standard error is often provided by software. For example, the Minitab display in Example 1 shows that sb1= 0.1289 (found in the column with the heading of SE Coeff and the row corresponding to the first predictor variable of the height of the mother). Use the sample data in Table 10-4 and the Minitab display in Example 1 to test the claim that
β1 = 0.
Step2 of 4:
We need to Use the sample data in Table 10-4 and the Minitab display in Example 1 to test the claim that β1 = 0. Also test the claim thatβ2 = 0. What do the results imply about the regression equation?
Step3 of 4:
We have multiple linear regression that is
Daughter = 7.5 + 0.707mother and
Daughter = 7.5 + 0.164father.
1).Consider the appropriate null and alternative hypothesis are
Consider,
Test statistics of t is given by t =
Where,
= 0.707