B.13 regression of a slope
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This document discusses how to conduct a hypothesis test for the slope of a regression line. It explains that the test determines if there is a significant linear relationship between an independent and dependent variable. The null hypothesis states that the slope is equal to zero, while the alternative is that it is not equal to zero. The test involves calculating the slope, standard error of the slope, and t-statistic to determine the p-value for comparing to the significance level and deciding whether to reject the null hypothesis.
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B.13 regression of a slope
- 2. Hypothesis Test for Regression Slope • Test is used to conclude whether there is a significant linear relationship between the independent variable X and the dependent variable Y. • Regression Line: Y= a + bx • a= Constant • b= Slope (regression Coefficient) • If the slope of the regression line is significantly different from zero, then we can determine that there is a significant relationship between the independent and dependent variables
- 3. Conditions • Standard requirements for simple linear regression – Dependent variable Y has a linear relationship to independent variable X – For each value of X, the probability distribution of Y has the same standard deviation – For any given value of X: • Y values are independent • Y values are normally distributed
- 4. Conducting a Hypothesis Test 1- State the Hypothesis Ho: b = 0 * the slope will not equal zero when there exists Ha: b = 0 a significant linear relationship between the independent and dependent variables 2- Form Analysis Plan * use a linear regression t- test to conclude whether the slope of the regression line differs significantly from zero. 3- Must find: SE of slope Slope of linear regression * DF= n-2 n= sample size * TS: t = b b= slope SE SE = Standard Error of Slope **P- value- probability of observing the sample statistic as extreme as the TS where the TS uses a t-score 4- Interpret: Given the null hypothesis, if the sample results are unlikely, then reject the null. (done by comparing the P-value to the significance level and rejecting the null hypothesis if the P-value is less than the significant level)