Question

7. A doctor w ted to determine whether there is a relation between a male's age and his HDL (so called good) cholesterol. The doctor randomly selected 17 of his patients and determined the HDL cholesterol. The data obtained by the doctor is the in the datatable below. Complete parts (a) through (below Click the icon to vew the data obtained by the doctor (a) Draw a scatter diagram of the data, treating age as the explanatory variable What type of relation, if any, appears to exist between age and HDL cholesterol? O A. The relation appears to be nonlinear OB. There does not appear to be a relation O C. The relation appears to be linear (b) Determine the least squares regression equation from the sample data (Round to three decimal places as needed (c) Are there any outliers or influential observations? O No O Yes (d) Assuming the residuals are normally distributed test whether a linear relation exists between age and HDL cholesterol levels at the 001 level of significance What are the null and alternative hypotheses? O A Hg 1 0 H, P, F0 OB M P = 0 H, B,>0 OCH R = 0;H, B,0 Use technology to compute the Pale Use the Tech Help button for further assistance The P values (Round to three decimal places as needed AM Type here to search Pte 18/2019 a O

Answer 1

7.

Option C: The relation appears to linear.

Scatterplot of HDL Cholesterol(y) vs Age(x) HDL Cholesterol(y) - 30 40 40 50 60 Age(x)

(0) g = 53.410 – 0.1907 (c) Yes.

Scatterplot of HDL Cholesterol(y) vs Age(x) HDL Cholesterol(y) - 30 40 50 60 Age(x)

Since at least two points are far away from fitted line hence they are treated as outlier.

(d) Option A. Ho: Bo = 0, H1 : 81 +1. P - value = 0.334 Option C: Do not reject the null hypothesis because the P-value is greater than a = 0.01. (e) Lower limit= -0.596, Upper limit = 0.216 (f) Option C: No, because the null hypothesis was not rejected. A good estimate for the HDL cholesterol of this paitent is û = 53.410 - 0.190 * 42 = 45.43.

Age(x)	HDL Cholesterol(y)		SUMMARY OUTPUT
36	57
41	55		Regression Statistics
47	36		Multiple R	0.249445382
30	55		R Square	0.062222999
53	33		Adjusted R Square	-0.000295468
51	42		Standard Error	10.04184292
63	40		Observations	17
63	40
24	49		ANOVA
37	45			df	SS	MS	F	Significance F
65	60		Regression	1	100.3620366	100.3620366	0.995273906	0.334279253
28	54		Residual	15	1512.57914	100.8386093
50	35		Total	16	1612.941176
26	45
54	36			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
50	56		Intercept	53.40988667	8.831268078	6.047816259	2.23171E-05	34.58648434	72.233289
40	26		X Variable 1	-0.189931495	0.190381909	-0.997634154	0.334279253	-0.59572093	0.215857939