Testing Hypotheses About Regression Coefficients If the coeffi...

Question

Testing Hypotheses About Regression Coefficients If the coefficient has a nonzero value, then it is helpful in predicting the value of the response variable. If 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 use the test statistic Critical values or P-values can be found using the t distribution with degrees of freedom, where k is the number of predictor variables and n is the number of observations in the sample. The standard error is often provided by software. For example, see the accompanying StatCrunch display for Example 1, which shows that (found in the column with the heading of “Std. Err.” and the row corresponding to the first predictor variable of height). Use the sample data in Data Set 1 “Body Data” and the StatCrunch display to test the claim that Also test the claim that What do the results imply about the regression equation?

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Accepted Answer

Hi, everyone. Let's take a look at this practice problem. This problem says a researcher develops a multilinear regression model to predict a person's lung capacity in liters based on their age, in years, and chest circumference in centimeters. The regression output from statistical software is shown below, and we're given a table where the first column is labeled as parameter and it has the values of intercept age and chest circumference. The next column is labeled estimate, and it has the values of 0.8564 minus 0.0237 and 0.1082. The next column is labeled standard error, and it has the values of 0.4290, 0.0061, and 0.0129. The next column is labeled alternative, and it has the values of not equal to 0, not equal to 0, and not equal to 0. The next column is labeled DF, which has the values of 117, 117, and 117. The next column is labeled T stat. And it has the values of 1.9963 minus 3.8852 and 8.3853. And the final column is level P value, and it has values of 0.0486, 0.0002, and less than 0.0001. Test the claim that H is not a useful predictor in lung capacity. Use the p-value to conclude at the 0.05 significance level. So the first thing we want to do is to write down our hypotheses. So for a null hypothesis H knot. We're going to have the claim that beta 1 is going to be equal to 0. Beta 1 is our first parameter which corresponds to age. And this would actually mean that age is not. A useful predictor. For lung capacity. And our alternative hypothesis, H1 is going to be with beta 1, not equal to 0, which would mean that it is a useful predictor. So we're told to use the P-value to conclude at the 0.05 significance level. And so that means we're gonna need to look up in our table here, our P value for our age. So that corresponds to the 2nd row under the column P-value. So that means that our P value in this case, is going to be equal to 0.0002, and that is actually less than our significance level of 0.05. So this means that we're going to actually reject our null hypothesis. So we're going to reject Hkno. So what that means is, At the 0.05 significance level, there is sufficient evidence to support the claim that age is a useful predictor of lung capacity. So that's going to be our answer for this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Hypothesis Testing

P-value

Standard Error

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