Question

Consider the following data: Hint (sx = 3.9, sy = 41.5, r = 0.879)

Height (Inches)	Weight (Pounds)
62	142
71	205
73	225
65	118
64	130
67	195
68	190

(a) Create a scatter plot of height (X-Axis) versus weight (Y-Axis)

(b) Calculate the Coefficient of Correlation

(c) Perform a test of the relationship: Ho: ρ= 0.0 with α = 0.05

(d) Estimate the slope of the Regression Line

(e) Estimate the Y-Intercept

(f) Calculate the Coefficient of Determination, r2.

(g) Provide an interpretation of r2.

Answer 1

(a)

Following is the scatter plot:

(b)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	62	142	3844	20164	8804
	71	205	5041	42025	14555
	73	225	5329	50625	16425
	65	118	4225	13924	7670
	64	130	4096	16900	8320
	67	195	4489	38025	13065
	68	190	4624	36100	12920
Total	470	1205	31648	217763	81759

Sample size: n = 7

Now,

The coefficient of correlation is :

(c)

Hypotheses are:

Test statistics:

-------------------------

Here degree of freedom is df=n-2=5 so p-value of the test is 0.0091.

Since p-value is less than 0.05 so we reject the null hypothesis.

The excel function used for p-value is: "=TDIST(4.128,5,2)"

(d)

Slope of the regression equation is

(e)

The intercept of the equation will be

So the regression equation will be

y'= -457.374 + 9.376*x

(f)

The coefficient of determination is:

(g)

The R- square shows that 77.32% of variation in dependent variable is explained by independent variable.