Question

In: Statistics and Probability

#AIDS Cases Diagnosed #AIDS Deaths 319 121 1170 453 3076 1482 6240 3466 11776 6878 19032...

#AIDS Cases Diagnosed	#AIDS Deaths
319	121
1170	453
3076	1482
6240	3466
11776	6878
19032	11987
28564	16162
35447	20868
42674	27591
48634	31335
59660	36560
78530	41055
78834	44730
71874	49095
68505	49456
59347	38510
47149	20736
38393	19005
25174	18454
25522	17347
25643	17402
26464	16371

3) Estimate a regression line Y = intercept + slope X. What are the intercept and the slope? Write the equation of the line you estimated.

4) Discuss the regression results. What does the slope mean?

5) What is the correlation coefficient equal to?

6) Do a hypothesis test in which the null hypothesis is that the correlation coefficient is equal to zero agains the alternative that it is different from zero. What is the test statistic? What is the p-value? What is your conclusion?

Expert Solution

In excel install analysis tool pak go to

Data >data analysis >regression

you will get

Output:

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.974616
R Square	0.949877
Adjusted R Square	0.947371
Standard Error	3588.723
Observations	22

ANOVA
	df	SS	MS	F	Significance F
Regression	1	4.88E+09	4.88E+09	379.0165	1.81E-14
Residual	20	2.58E+08	12878932
Total	21	5.14E+09

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	88.7161	1370.719	0.064722	0.949038	-2770.55	2947.986
#AIDS Cases Diagnosed	0.607351	0.031197	19.46835	1.81E-14	0.542276	0.672427

Regression equation is

AIDS Deaths=88.71609879+0.607351431*AIDS Cases Diagnosed

slope=0.607351431

y intercept=88.71609879

4) Discuss the regression results. What does the slope mean?

R sq=0.949876755

=0.949876755*100

=94.99%

94.99% variation in AIDS Deaths is explained by model.Good model.

slope=88.71609879

y intercept=0.607351431

standard error =3588.722907

orchestra answered 1 year ago

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