Consider the simple population regression model where the treatment is the same for the members of the treatment group, and hence X is a binary variable. Explain why the coefficient on X represents the difference between two means. How is the test for the statistical significance of the coefficient on X related to the test for differences in means between two populations, when their variances are different? Write down the null and alternative hypothesis in each case.
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We have a simple population regression model with a binary treatment variable, K. So, the model can be written as: $$Y_i = \beta_0 + \beta_1 K_i + u_i$$ Show more…
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Text: Question 9 Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable) and X (independent variable). ANOVA df SS Regression 1 3328.312 Residual 8 10539.654 Total 9 13867.966 Coefficients Standard Error t Stat P-value Intercept 241.76 83.280 1.689 0.030 X 148.72 38.312 1.283 0.055 1. What is the estimated regression equation that relates y to x? 2. Is the regression relationship significant? Use a p-value and alpha = 0.04. 3. What is the estimated value of y if x = 4.5? 4. Compute the value of the coefficient of determination and interpret its meaning. Be very specific.
Sri K.
4% a) Explain the practical meaning of the regression coefficient b1 = 0.189 for 'Income' in the context of this problem. 12% b) For the regression coefficient b1 for 'Income', we want to test the hypotheses Ho: b1 = 0.25 versus Ha: b1 < 0.25 at the 5% significance level. Find the degree of freedom, the critical value, and the test statistic. Perform the test and what is the test result? Based on the test result, what conclusion can be drawn about the relationship between Savings and Income? 10% c) Construct a 95% confidence interval for the regression coefficient for 'Income'. Also, explain the practical meaning of this interval in the context of this problem.
Consider the regression model: Yi = Bo + B1xi1 + B2Xi2 + B3xi3 + ui. Explain in detail how you would test the following hypotheses: (a) Ho: B1 = B2 = 0 (b) Ho: B1 = B2
Adi S.
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