Question

Given the following sample observations, create a scatter diagram using Excel. 8 -16 12 18 У 58 247 153 3 341 Click here for the Excel Data Fils 1. Compute the correlation coefficient. (Round your answer to 3 decimal places.) Coefficient of correlation 2. Does the relationship between the variables appear to be linear? Yes No 3. Try squaring the X variable and then determine the correlation coefficient. (Round your answer to 3 decimal places.) Coefficient of correlation Y87 Y52 3 4534 1 -8-10 12 2 18 12345678

Answer 1

Hereis the scatter plot between x and y

400 50 0 -20 -15-10 -5 10 15 20

Now we will perform excel regression analysis.

FIrst put the value of x and y in two differnet column.

Then go to data -> data analysis -> Regression

Fill input Y Range and Fill input x range and then click ok.

Following is the summary.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.2975
R Square	0.088506
Adjusted R Square	-0.21532
Standard Error	151.3881
Observations	5
ANOVA
	df	SS	MS	F
Regression	1	6676.14	6676.14	0.291301
Residual	3	68755.06	22918.35
Total	4	75431.2
	Coefficients	Standard Error	t Stat	P-value
Intercept	155.7166	68.25663	2.281341	0.106803
x	2.927105	5.423345	0.539723	0.626875

Here r = 0.298

(2) as we see the ANOVA table the significance F is greater than 0.05.

so the relationship is not linear.

(3) Now for part (3) we will use indepdentn variable as x²

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.997501
R Square	0.995008
Adjusted R Square	0.993343
Standard Error	11.2039
Observations	5
ANOVA
	df	SS	MS	F
Regression	1	75054.62	75054.62	597.9147
Residual	3	376.5819	125.5273
Total	4	75431.2
	Coefficients	Standard Error	t Stat	P-value
Intercept	-3.7281	8.376083	-0.44509	0.686412
x^2	1.036162	0.042375	24.45229	0.00015

so here new coefficient of correlation  = 0.998