QUESTION 04 (20 points)-Simple Linear Regression (SLR) We have the following hyp

Question

QUESTION 04 (20 points)-Simple Linear Regression (SLR) We have the following hypothetical data for the independent variable x (other names regressor, covariate, or explanatory variable) and the dependent variable y (regressand). Table 4.1 Data and Important Terms 7.54 6.27 3.17 1.65 3.84 1.71 1.78 39.31290 9.88350 5.99 2.53 TOTAL 22.47000 17.16000 (a) Use Excel to draw a y-x scatter diagram with y on the vertical axis. Add the linear trend line. (b) Complete Table 4.1. Use 5 decimals throughout your calculations if applicable. (c) Give an equation for and manually calculate the slope bi Table 4.1 aids your calculations (d) Give an equation for and calculate the y-intercept bo. Write the sample regression equation. (e) Calculate sample average x-bar and manually calculate predicted value for y at x-bar (f) Manually calculate predicted value for y at 7.0 (within data range interpolation). () Manually calculate predicted value for y at x = 1.0 (outside data range extrapolation). Table 4.2 Predicted Values and Variations 7.54 6.27 3.17 1.65 3.84 1.71 1.78 5.15 5.99 2.53 2.72910 5.57914 194812 TOTAL (h) Complete Table 4.2. Use 5 decimals. The symbol (means "no need to fill in. (i) Give an equation for and manually calculate the standard error of estimate s(x.y). G) Find SST and SSE in Table 4.2. Then, calculate SSR. Calculate the degrees of freedom for these three statistics: df SST),dissR), and dftSSE) (k) Give an equation for the coefficient of determination in terms of SSR and SST, Give another equation for r in terms of SSE and SST. Calculate in either way and comment on (I) Give an equation for the adjusted coefficient of determination r( adj), Calculate F( adi). (m) Give an equation for and calculate the F-statistic in the ANOVA test of Holthere is no linear relationship between x & y) versus H(there exists a linear relationship between x & y). Calculate the degrees of freedom df for this F-statistic. Use Excel to calculate the corresponding p-value. (n) Give an equation for and calculate the estimated standard deviation of the slope s(b) (o) Give an equation for and calculate the t-statistic to test Ho(.) vs Hilf, z 0). Calculate the degrees of freedom for this t-statistic. Use Excel to calculate the corresponding p-value. (p) Write the sample regressiorn in the format: (t-statistic)* This format is typically presented in a report's main text. In addition, the corresponding table of full regression results can be put in the appendix. For the number of stars besides the t-statistic, use this rule: * for palue s 0.01; *for 0.01 p-values0.05; *for 0.05 p-values0.1

Explanation / Answer

Part B x y x2 xy 1 7.54 1.71 56.85160 12.89340 2 6.27 1.78 39.31290 11.16060 3 3.17 5.15 10.04890 16.32550 4 1.65 5.99 2.72250 9.88350 5 3.84 2.53 14.74560 9.71520 Average 4.494 Part A use scatter diagram x,y for preparing the chart. click on the dots to add trendline which will be linear in this case. Also select add equation to get the line equation. Here cannot attach copy the chart along with excel. Part C y=-0.755x+6.8248 slope -0.755 Part D Intercept 6.8248 Part e X, Average 4.494 using eq in part C y 3.43183 part f at x=7 dx/dy=slope or (7.54-7)=-0.755*(1.71-Y), calculate the value of Y or Y=2.425 Part g at x=1 dx/dy=slope or (1.65-1)=-0.755*(5.99-Y), calculate the value of Y or Y=6.851

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