Question

An article gave a scatter plot along with the least squares line of x = rainfall volume (mº) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot. x 4 12 14 16 23 30 40 51 55 67 72 80 96 112 127 y 4 10 13 46 53 72 82 99 15 15 25 27 44 38 103 in USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? Yes, the scatterplot shows a reasonable linear relationship. O Yes, the scatterplot shows random scattering with no pattern. No, the scatterplot shows a reasonable linear relationship. No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 51. (Round your answer to four decimal places.) (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) m3 (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)

Answer 1

c) For x= 51

. A B C D E F - H j K L M N o P Q 1 X Y 2 4 4 SUMMARY OUTPUT 3 12 10 4 5 14 16 23 13 15 15 6 Regression Statistics Multiple R 0.9893 R Square 0.9787 Adjusted R Square 0.9771 Standard Error 4.9404 Observations 15 Y 25 7 8 9 30 40 120 27 44 100 10 38 11 46 ANOVA 80 12 51 55 67 72 80 96 112 53 df 60 Significance F 0.0000 13 72 1 SS MS F 14573.6345 14573.6345 597.0940 317.2989 24.4076 14890.9333 . 40 14 Regression Residual Total 82 99 13 15 14 20 . 16 127 103 0 17 t Stat P-value Lower 95% 0 20 40 60 80 100 120 140 18 Coefficients Standard Error -1.6614 2.2311 0.8397 0.0344 -0.7447 Intercept х 0.4697 -6.4814 0.7655 Upper 95% 3.1585 0.9139 х 24.4355 0.0000 19 20

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d) Point estimate of the standard deviation is 4.94

e) The proportio of the observed variationis runoff volume that can be explained by rainfall volume is given by coefficient of determination which is 0.9787