Use the data given below to perform a regression through the origin and answer q

Question

Use the data given below to perform a regression through the origin and answer questions 1 – 3.

      X

      Y

5

4

6

3

1

2

4

6

2

3

Source

Df

SS

MS

Regression

1

59.76

59.756

Error

A

14.24

3.561

Total

B

C

Fit the model Y = 1X + . What is your predicted value of 1? (Round your answer to three decimal places)

What should be the value of A, the degrees of freedom for error, in the ANOVA table for the regression through the origin?

What should be the value of C, total sum of squares, in the ANOVA table?

      X

      Y

5

4

6

3

1

2

4

6

2

3

Explanation / Answer

(1) Using r-software,

R-code to fit a linear model:

x=c(5,6,1,4,2)
y=c(4,3,2,6,3)
lm(y~x)

Output:

Call:

lm(formula = y ~ x + 0)

Coefficients:
x
0.8537

Hence, fitted model is ,

y=0.8537*x

(2) Here,predicted value of 1 =0.8537

(3) The value of A, the degrees of freedom for error, in the ANOVA table for the regression through the origin=Number of observations -1=5-1=4

(4) The value of C, total sum of squares, in the ANOVA table=59.76+14.24=74

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