m3 and y = runoff volume m3 An article gave a scatter plot along with the least

Question

m3 and y = runoff volume m3 An article gave a scatter plot along with the least squares line of x = rainfall volume read from the plot. for a particular location. The accompanying values were x 7 12 14 18 23 30 40 47 55 67 72 84 96 112 127 4 10 13 15 15 25 27 47 38 46 53 67 8299 101 (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows a reasonable linear relationship. O Yes, the scatterplot shows a random scattering with no pattern O No, the scatterplot shows a reasonable linear relationship. O 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 five decimal places.) slope intercept -1.58615X 0.82810 (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 47. (Round your answer to four decimal places.) m3 (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.) Need Help?Read It Talk to a Tutor

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -1.5863724 + 0.82810396 x
Sample size: 15
R (correlation coefficient) = 0.98789314
R-sq = 0.97593286
Estimate of error standard deviation: 5.1640231

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b) Slope = 0.82810

Intercept = -1.58637

c) Predicted average = 37.3345

d) Point estimate = 5.16

e) Proportion of variation attributed = 0.9759

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -1.5863724 2.3484316 ? 0 13 -0.67550292 0.5112 Slope 0.82810396 0.036067453 ? 0 13 22.959868 <0.0001

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