I cant get this question right. It would be great if somone could help me. Thnak

Question

I cant get this question right.

It would be great if somone could help me.

Thnak you.

An article gave a scatter plot along with the least squares line of x = rainfall volume (m^3) and y = runoff volume (m^3) for a particular location. The accompanying values were read from the plot. 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. Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to five decimal places.) slope intercept Calculate a point estimate of the true average runoff volume when rainfall volume is 50. (Round your answer to four decimal places.) m^3Calculate a point estimate of the standard deviation a. (Round your answer to two decimal places.) m^3 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

Let x = rainfall volume

y = runoff volume

b) In EXCEL we directly find slope and intercept.

Syntax :

=SLOPE(known y's, known x's)

=INTERCEPT(known y's, known x's)

where known y's is the array of y-observations.

known x's is the array of x-observations.

slope = 0.8426

intercept = -1.9313

The slope is positive indicates that there is positive correlation between x and y.

The regression equation is,

y = -1.9313 + 0.8426*x

c) When x = 50 then y = ?

y = -1.9313 + 0.8426*50 = 40.1982

Here for finding standard deviation we can use MINITAB.

steps :

STAT --> Regression --> Regression --> Response : y --> Predictors : x --> Result : select second option --> ok

Regression Analysis: y versus x

The regression equation is
y = - 1.93 + 0.843 x

Predictor Coef SE Coef T P
Constant -1.931 2.421 -0.80 0.439
x 0.84259 0.03706 22.73 0.000

S = 5.31731 R-Sq = 97.5% R-Sq(adj) = 97.4%

Analysis of Variance

Source DF SS MS F P
Regression 1 14614 14614 516.88 0.000
Residual Error 13 368 28
Total 14 14982

S is the standard error.

S = 5.31731

S = sd / sqrt(n)

n = number of data pairs. = 15

5.31731 = sd / sqrt(15)

sd = 20.594

e) In this part we have to calculate Rsq .

Rsq = 97.5%

It expresses the proportion of the variation in y which is explained by variation in x.

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