2. Simple Linear Regression: Estimation Theory gives you the following relations

Question

2. Simple Linear Regression: Estimation Theory gives you the following relationship between variables a and y: You collect a sample of data on n = 3 sample members. The data are: 1. Estimate the relationship between a and y using this sample. What is 2. Write down the relationship between the mean of y and the mean of z in (zi, yl)-(6,5), {r2,Y2)-(-2,8), and {r3,m) = {2,7} your estimate of A)? of '? terms of your estimates, what is your prediction for y when x = 10? 3. Calculate the residuals úl , for i = 1, 2, 3, of this regression. 4. Caleulate the sum of squared residuals (SSR) and total sum of squares SST). 5. Calculate R-squared. What does R-squared measure? What is the range of possible R-squared values? What does the R-squared you calculated tell you?

Explanation / Answer

1)

y^ = 7.41666 -0.375 *x

b0 = 4.16666

b1 = -0.375

2) y^ when x = 10

y^ = 7.41666 -0.375 *10 = 3.66666

3)

4)

SSR = 1

SST = 2

5)

R^2 = 0.964285

0< R^2 <= 1

this means 96.43 % of variation in the dependent variable is explained by this model .

Please rate

SUMMARY OUTPUT Regression Statistics Multiple R 0.981980506 R Square 0.964285714 Adjusted R Square 0.928571429 Standard Error 0.40824829 Observations 3 ANOVA df SS MS F Significance F Regression 1 4.5 4.5 27 0.121037718 Residual 1 0.166666667 0.166666667 Total 2 4.666666667 Coefficients Standard Error t Stat P-value Lower 95% Intercept 7.416666667 0.276385399 26.83450967 0.023712948 3.904857198 x -0.375 0.072168784 -5.196152423 0.121037718 -1.291991341 RESIDUAL OUTPUT Observation Predicted y Residuals 1 5.166666667 -0.166666667 2 8.166666667 -0.166666667 3 6.666666667 0.333333333

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