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

Question

An article gave a scatter plot along with the least squares line of x = rainfall volume (m3) 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 46 55 67 72 81 96 112 127

y    4 10 13 15 15 25 27 48 38 46 53 67 82 99 102

1. Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to five decimal places.

a) slope

b) intercept

2. Calculate a point estimate of the true average runoff volume when rainfall volume is 50. (Round your answer to four decimal places.

3. Calculate a point estimate of the standard deviation . (Round your answer to two decimal places.)

4. 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.)

x    4 12 14 16 23 30 40 46 55 67 72 81 96 112 127

y    4 10 13 15 15 25 27 48 38 46 53 67 82 99 102

1. Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to five decimal places.

a) slope

b) intercept

2. Calculate a point estimate of the true average runoff volume when rainfall volume is 50. (Round your answer to four decimal places.

3. Calculate a point estimate of the standard deviation . (Round your answer to two decimal places.)

4. 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

Using Simple Linear Regression Model : Y = beat0 +beta1x+Error

a)Slope : 0.82513

b)Intercept : -0.799

2) Equation : Runoff Volume = - 0.80 + 0.825 Rainfall Volume If Ranifall volume 50 Answer is 40.4550

3) Standard Deviation : 5.4996 ( Standard deviation = Standard Error * Sqrt(n))

4) 97.3161% variation explained by this modle .

Regression : 14141

Residual error : 390

Total Variation : 14531

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