Question

Use the data sct below to answer the following questions a) Compute r(x, y). b) Compute the slope of the regression line c) Compute the intercept of the regression line d) Plot the residuals. Is a linear model appropriate for the data?

Answer 1

	X	Y	X * Y	X2	Y2
	1	2	2	1	4
	2	2	4	4	4
	3	5	15	9	25
	4	4	16	16	16
	5	6	30	25	36
Total	15	19	67	55	85

Correlation coefficient is

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$

$r = ( ( 5 * 67 ) - 15 * 19 ) / ( \sqrt{ ( 5 * 55 ) - ( 15 )^{2} )( 5 * 85 ) - ( 19 )^{2} })$

Part b)

Equation of regression line is $\hat{Y} = a + bX$

$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = 1

$a =( \Sigma Y - ( b * \Sigma X) ) / n$
a =( 19 - ( 1 * 15 ) ) / 5
a = 0.8

Equation of regression line becomes   $\hat{Y} = 0.8 + 1X$

Slope = 1

Y intercept = 0.8

Part d)

Since the residual plot is random i.e residual does not follow any pattern.

We can say that the model is appropriate to the data.