Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept) age height forearm Estimate 10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value 2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedom Multiple R-squared: 0.01983, Adjusted R-squared: -0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 What is the test-statistic is used to test whether at least one of the explanatory variables is a significant predictor of the response variable? 2.259 -0.332 0.5731 0.884 -0.946
Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables:
shoe size – in inches
age – in years
height – in inches
forearm length – in inches
Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows:
| > summary(lm(shoesize ~ age + height + forearm, data = measures)) | ||||
| Coefficients: | ||||
(Intercept) age height forearm |
Estimate 10.14882 0.06045 -0.02108 -0.06479 |
Std. Error 4.49245 0.06838 0.06350 0.06847 |
t value 2.259 0.884 -0.332 -0.946 |
Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 |
| Residual standard error: 1.719 on 85 degrees of freedom Multiple R-squared: 0.01983, Adjusted R-squared: -0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 |
What is the test-statistic is used to test whether at least one of the explanatory variables is a significant predictor of the response variable?
2.259
-0.332
0.5731
0.884
-0.946
In order to check the overall significance or the adequacy of regression model in predicting the value of dependent variable, a F-test needs to be conducted.
The hypotheses test will contain two hypotheses: null hypothesis and alternate hypothesis. The alternate hypothesis is about the claim which is to be tested. If p-value<α, where, α is significance level, then null hypothesis can be rejected and it can be concluded that test is significant.
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