Predict output for test dataset using the fitted model. Perform Linear Regression to predict housing values based on medianincome. The last section of the regression summary provides the standard deviation about the regression ( residual standard error), the square of the correlation coefficient ( multiple R-squared), and the result of an F-test on the model’s ability to explain the variation in the y values. Perform Linear Regression with one independent variable : Extract just the medianincome column from the independent variables (from Xtrain and Xtest). The results of these t-tests provide convincing evidence that the slope is not zero, but no evidence that the y-intercept differs significantly from zero. Clicking OK generates the information shown in Figure \(\PageIndex \beta_0 \neq 0\) In other words, there is no statistically significant relationship between the predictor variable, x, and the response variable, y. For a one-unit change in age, on average, the Brozek percent fat increases by 0.03, after. Select the radio button for Output range and click on any empty cell this is where Excel will place the results. For the above example output, the hypothesis that the coefficient on TB3 is zero is rejected at the 5 significance level but not at the 1 level. Simple linear regression uses the following null and alternative hypotheses: H 0: 1 0 H A: 1 0 The null hypothesis states that the coefficient 1 is equal to zero. When testing the null hypothesis that there is no linear association between Brozek percent fat and age after adjusting for fatfreeweight and neck, we fail to reject the null hypothesis (t 1.162, df 248, p-value 0.246). Excel’s summary output uses the x-axis label to identify the slope.
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