Question

Regression Equation:

Y' 1.15X+ -5.688
Display the data with a scatterplot inserting a regression line. Make comments on the arrangements of the points

Predicted values of Y: 0.062, 1.212, 2.362, 2.362, 2.362, 3.512, 3.512, 3.512, 3.512, 4.662

Residual: 0.938, -0.212, -0.362, -0.362, -0.362, -1.512, -0.512, -0.512, 1.488, 1,338

Answer 1

The residual of regression line is = e = observed value - predicted value.

So, for each predicted value and the corresponding residual, we can find the observed value for it.

Then, using the linear regression equation and the values of predicted values, we can find values of X using -

X = ( 5.688 + Y' ) / 1.15

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We would get the following data for X and Y -

Predicted Values (Y')	Residual (e)	X = (5.688 + Y')/1.15	Y = e + Y'
0.062	0.938	5	1
1.212	-0.212	6	1
2.362	-0.362	7	2
2.362	-0.362	7	2
2.362	-0.362	7	2
3.512	-1.512	8	2
3.512	-0.512	8	3
3.512	-0.512	8	3
3.512	1.488	8	5
4.662	1.338	9	6

And the scatter plot with fitted line is as shown -

There are 3 points lying on the same vertical line at x = 8. It indicates that this is a repeated measure value of X. The positive trend is however clearly visible because as the value of independent variable increases, the value of dependent variable also increases.