Because the conditions check, you will be calculating a t-test for the slope of the regression line at the α = 0.05 significance level. H0: β=0 Ha: β≠0 Conditions: It is stated you have the conditions necessary for inference for linear regression. Parameter: Let β equal the true slope of the regression line for predicting the second-round score from the first-round score. We have sufficient evidence that there is a linear relationship between the first-round score and the second-round score. Then, perform a linear regression t-test using the data, and obtain t = 6.9477 and p = 3.9583 × 10^-5 = 0.0000396 Conclusion: Because p = 0.0000396 is less than α = 0.05, we reject the null hypothesis. Calculations: Using a Calculator: First, find the least-squares regression line using your calculator with the result ŷ = 5.8088 + 0.9343x, where x represents the round-one score and ŷ represents the predicted round-two score. Random: The problem states 12 college-age female golf players were selected randomly. Equal variance: The residual plot shows an equal amount of scatter around the horizontal line. Normal: The histogram of the residual is unimodal and roughly symmetric. You can assume there are at least 10(12) = 120 college women's golf players. Independent: Each golf player is independent of the others. The residual plot also shows a random scatter of points about the residual line. H0: β=0 Ha: β≠0 Conditions: Linear: The scatterplot shows a clear linear form. Conclusion: You will provide the same conclusion as all other hypotheses tests based on the p-value and significance level (reject the null hypothesis or fail to reject the null hypothesis) in terms of the context of the problem. ![]() Computer Output: Most linear regression inference questions will include a computer printout for you to use to obtain your statistics. The calculator gives you the values of t, p, df, a, b, s, r2, and r. Choose the appropriate alternative hypothesis. Step 3: Enter the appropriate list names for Xlist and Ylist, and enter 1 for Freq (unless you know you have a different frequency). Step 2: Select, highlight TESTS, then choose option F:LinRegTTest. Calculations By hand: in photo Using GC: t-Test for Slope of a Regression Line Step 1: Enter the explanatory variable, x, into L1, and the response variable, y, into L2. When the conditions are met, use a t-test for the slope of the regression line. You must be told the data were produced in these ways. Random: Data must come from a well-designed random sample or randomized experiment. In the residual plot, we must see equal scattering both above and below the line. Equal variance: For each given value of x, the standard deviation of y must remain the same. Create a Normal probability plot, histogram, or stemplot of the residuals and check for Normality. ![]() Normal: For each given value of x, the values of the response variable, y, must vary according to a Normal distribution. The data must be from random sampling and random assignment to ensure independence. ![]() Independent: Check that for each given value of x, the values of the response variable, y, are independent of each other. Create a scatterplot of the data to check the overall pattern is linear. The mean response of the y values for the fixed values of x are related linearly by the equation μy=α+βx. Linear: Verify that the relationship between x and y is linear. Try using the mnemonic LINER (linear, independent, Normal, equal variance, and random) to recall these new conditions. Conditions The conditions for a significance test for slope of a regression line have the most significant differences when compared with the other types of significance testing. The last two options allow you to determine whether the data are related positively or negatively. However, it can also be written as Ha: β≠β0 Ha: β>0 Ha: β<0. The alternative hypothesis is most often two-sided, with Ha: β≠0, meaning there is a linear relationship. If the slope of the line is zero, then there is no linear relationship between the x and y variables. Most often, you will determine whether the slope of the regression line is equal to zero, making the null hypothesis H0: β=0. Parameter Let β equal the true slope of the regression line for predicting y from x.
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