Area of House (hundreds of square feet) Selling Price (thousands of dollars) 20

Question

Area of House (hundreds of square feet) Selling Price (thousands of dollars) 20 250 19 220 27 350 28 390 30 320 15 200 25 360 23 290 18 210 35 410 (a) Do a scatter diagram for the data, insert the trend line and add the equation and R2 value to the diagram. (b) Find SSxx, SSyy and SSxy. (c) Determine the correlation coefficient. Comment on the value of the correlation coefficient. (d) Find the regression equation manually. Compare with the equation obtained when doing the scatter diagram. (e) Find SST, SSR and SSE. (f) Find the degrees of freedom associated with the sum of squares in part (e). (g) Find MSR and MSE. (h) Summarize your findings as an ANOVA table. (i) Find the coefficient of determination R2. (j) Find standard error of the estimate se (k) Test the hypothesis that Y and X are not related. That is, test H0: ?1 = 0 vs. H1: ?1 ? 0 by using a t-statistic. Use ? = 0.05. (l) Find the predicted value of Y given X = 24. Give an interpretation of the predicted value in the context of the problem. (m) Find a 95% confidence interval for the mean value of Y given X = 24. Give an interpretation of the confidence interval in the context of the problem. **please show work

Explanation / Answer

similar problem:-how do I calculate SSE with the following information
y^ = 2.1 + 3.4x xbar = 2.5. ybar = 10.6 SSxx = 4.77 SSyy = 59.21 SSxy = 16.22 n = 20 I have been looking it up everywhere but everything says I need actual values of y (yi's if you will). My problem does not give me any specific values of x or y. I also need to calcuate s and s squared from this as well

solution:-
Compute the correlation coefficient r

r = Sxy / Sx Sy

r = (16.22) / (4.77)( 59.21) = 0.0574298

r^2 = 0.003298


r^2 = SSR/ SST
SSR = regression sum of squares
SST = Total sum of squares = Syy = 59.21

r^2 = SSR/ SST
0.003298 = SSR / 59.21

SSR = (59.21)(0.003298) = 0.19527458

SST = SSR + SSE
SSE = 59.21 - 0.1953 = 59.0147
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Is S the standard deviation of Y ? If so,

S^2 = SSyy / n = 59.21/20 =2.9605 (some people use n-1 = 19)
S = sqrt(2.9605) = 1.7206

If S is the standard deviation of X,
S^2 = SSx/ n = 4.77/20 = 0.2385
S = sqrt(0.2385) = 0.4884

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