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	8	12	14	18	23	30	40	47	55	67	72	82	96	112	127
y	4	10	13	14	15	25	27	48	38	46	53	75	82	99	101

(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 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 five decimal places.)

slope
intercept

(c) Calculate a point estimate of the true average runoff volume when rainfall volume is 52. (Round your answer to four decimal places.)
m³

(d) Calculate a point estimate of the standard deviation σ. (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

a)

Yes, the scatterplot shows a reasonable linear relationship

b)

slope =0.84503

intercept =-1.90368

c)

predicted val=-1.90368+52*0.84503=

42.0379 (please try 42.0376 if this comes wrong)

d)

SST =                   'Σ(Yi-Y̅)2                 =		14917.333
SSR =                   'Σ(Ŷ-Y̅)2                 =		14488.237
SSE =                   'Σ(Yi-Ŷ)2                 =		429.0968

	s2 =SSE/(n-2)=	33.0074
std error σ              =	=se =√s2=	5.75

e)

Coeffficient of determination R^2 =SSR/SST=

0.9712