An article gave a scatter plot along with the least squares line of x = rainfal

Question

An article gave a scatter plot along with the least squares line of x = rainfal volume (m3) and y = runoff volume (m*) for a particular location. The accompanying values were read from the plot. x 5 12 14 18 23 30 40 46 55 67 72 85 96 112 127 y 4 10 13 14 15 25 27 48 38 46 53 67 82 99 105 (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. Yes, the scatterplot shows a random scattering with no pattern No, the scatterplot shows a reascnable linear relationship. No, the scatterplot shews a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to five decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 49. (Round your answer to four decimal places.) (d) Calculate a point estimate of the standard deviation . (Round your answer to two decimal places.) (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.)

Explanation / Answer

b] y = -1.7226 + 0.8377 x

c] x=49

y = -1.7226 + 0.8377 *49

   y = 39.3247

e] 97.46% variation in runoff volume can be attributed to the SLR relationship between runoff and rainfall.

Regression Statistics Multiple R 0.9872564 R Square 0.97467521 Adjusted R Square 0.97272715 Standard Error 5.39678881 Observations 15 ANOVA df SS MS F Significance F Regression 1 14572.30405 14572.3 500.331 9.21496E-12 Residual 13 378.6292835 29.12533 Total 14 14950.93333 Coefficients       Standard Error t Stat         P-value Intercept -1.72256217 2.439505014 -0.70611 0.49258 x 0.83770378 0.037450859 22.36808 9.21E-12

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