My Notas O Ass Your An article gave a scatter plot along with the least squares

Question

My Notas O Ass Your An article gave a scatter plot along with the least squares ine of x rainfall volume (m2) and y runoff valume (m2) for a particular location. The accompanying values were read from the plot x 5 12 14 19 23 30 40 45 55 6 72 81 96 112 127 Y 4 10 13 15 15 25 27 48 38 46 53 68 82 99 105 (a) Does a scatter plot of the deta support the use of the simgle ineer regression mode? Yes, the scatterplot shows a reasonable lineer relationship. Yes, the scatterplot shows a random scattering with no pattern. No, the scatterplot shows a reasonable lineer relationship. No, the scatterplot shows a random scettering with no pattern (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your enswers to five decimal places.) slope intercept c) Calculate a point estimate of the true average runom volume ahen rartam vefume is 52. (Round your answer to four deoma pikes) m2 (d) Calculabe a point estimate of the standard deviation o.(Round your answer to two decimal places.) (e) What proportion of the observed variation in nunoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.) Need Help? Tetter

Explanation / Answer

The statistifcal software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -1.6462509 + 0.84297464 x
Sample size: 15
R (correlation coefficient) = 0.98675633
R-sq = 0.97368806
Estimate of error standard deviation: 5.4993949

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Option A is correct.

b) Slope = 0.84297

Intercept = -1.64625

c) Point estimate = 42.1884

d) Point estimate for standard deviation = 5.50

e) Proportion of explained variation = 0.9737

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -1.6462509 2.4893482 ? 0 13 -0.66131806 0.52 Slope 0.84297464 0.038433445 ? 0 13 21.933362 <0.0001

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