Q.3. A simple linear Regression is fit, relating Y to X. You find the following spreadsheet. | X | Y | Y-hat | Y-bar | |---|---|---|---| | 20 | 47 | 50 | 65 | | 20 | 53 | 50 | 65 | | 30 | 60 | 65 | 65 | | 30 | 70 | 65 | 65 | | 40 | 82 | 80 | 65 | | 40 | 78 | 80 | 65 | p.3.a. Compute: Regression Sum of Squares (SSR). Error Sum of Squares (SSE), and Total Sum of Squares (SSTO): SSR = ___________ dfr = ___________ SSE = ___________ dfE = ___________ SSTO = ___________ dfTO = ___________ p.3.b. What proportion of the variation in Y is "explained" by X? Answer = ______________________________________ p.3.c. What is the slope of this estimated regression line? Answer = ______________________________________ Q.4. True/False (Not related to Q.3): p.4.a. The width of a prediction interval for an individual case can be narrower than the corresponding confidence interval for the mean at the same Xh level and same ? level, based on the same fitted regression. True or False p.4.b. The Pearson Correlation Coefficient will always be the same sign as the slope coefficient. True or False p.4.c. If we obtain a 95% Confidence Interval for ?? to be (-1.2 , 3.6) the P-value for the F-statistic for testing H?: ?? = 0 versus HA: ?? ? 0 will be greater than 0.05 True or False p.4.d. If R% = 0, all of the observations fall on the fitted equation (with slope not equal to zero) True or False
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Question 4. (25 points) A simple linear regression of the form y = Β₀ + Β₁ X₁ applied to 17 (x,y) data points resulting in the values Β₀ = 6.54 and Β₁ = 1.23 for the y-intercept and slope, respectively. The standard error of the regression line sigma hat (̐̑) = 2.93, the variance of X = 2.60, and the variance of Y = 4.86. (Chapter 12) Note: Sxx = Var(X)*(n-1) and SYY = Var(Y)*(n-1) a) Given that the mean X = 2.8, what is the mean value of Y? b) What is the correlation r between X and Y? c) What is the R"-squared coefficient of determination for this regression line? d) Given that the t-statistic of the slope Β₁ equals 2.7 with 15 d.o.f., what is the F-statistic for this regression line? r = ̐Β₁ √(Sxx / SYY) so that the sample correlation coefficient is simply a scaled version of the estimated slope parameter ̐Β₁. Moreover, it turns out that r" = R" so that the square of the sample correlation coefficient is equal to the coefficient of determination of the regression model. This is because the F-statistic is the square of the t-statistic t" = F
Umar Sohail Q.
Text 1: You are given the following information about variables y and x: y x Dependent Variable Independent Variable -0.0 -7.2 8.2 3.7 -3.1 6.4 10.3 7.7 In addition, it is known that the slope of the regression line b1 = -2.6 The y-intercept b0 for the estimated regression equation equals ____ (round your answer to two decimal places). Text 2: Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained: y = 12 + 1.8x n = 25 sb1 = 0.2683 Using α = 10%, the critical t value for testing the significance of the slope is ____ Show your answer with three decimal places. Text 3: As a result of running a simple regression on a data set, the following estimated regression equation was obtained: y = 1.0 - 5.0x Furthermore, it is known that SSR = 760, and SSE = 131. Calculate the correlation coefficient R; round your answer to three decimal places.
Sri K.
A regression line is used for all of the following except which one? A. To estimate the average value of Y at a specified value of X. B. To predict the value of Y for an individual, given that individual's X-value. C. To estimate the change in Y for a one-unit change in X. D. To determine if a change in X causes a change in Y. 2. Which choice is not an appropriate description of a regression equation? A. Estimated response B. Predicted response C. Predicted outcome D. Observed response 3. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables? A. Compute a regression line from a sample and see if the sample slope is 0. B. Compute the correlation coefficient and see if it is greater than 0.5 or less than 0.5. C. Conduct a test of the null hypothesis that the population slope is 0. D. Conduct a test of the null hypothesis that the population intercept is 0. 4. In simple linear regression, when b is significantly different from zero we conclude that A. X causes Y B. There is a linear relationship between X and Y C. The relationship between X and Y is quadratic D. There is no relationship between X and Y 5. If a predictor variable, X, is found not to be statistically significant, we would conclude that? A. A change in y causes a change in x B. A change in x causes a change in y C. Changes in x are not associated with changes in y D. Changes in x are associated with changes in y 6. The ordinary least squares solution is represented by which of the following? A. Σ(X - Y)² B. Σ(Y - Ŷ)² C. Σ(X - Ŷ)² D. R²Σ(Y - Ŷ)² 7. For which of the following correlations would the data points be most widely scattered around the regression line? A. r = 0.10 B. r = 0.50 C. r = -0.80 D. There is no relationship between the correlation and how close the data points are to the regression line 8. One use of regression is to increase the accuracy of predicting Y scores. How much of the variability in the Y scores is predictable from the regression equation? A. r² B. 1 - r² C. r D. 1 - r
Krishna G.
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