The Coronary Artery Initiative was founded to investigate the causes of hypercho

Question

The Coronary Artery Initiative was founded to investigate the causes of hypercholesterolemia, a condition known to be a risk factor for atherosclerosis and heart attacks. The scientists decided to focus on cigarette smoking (sticks per day) and sedentariness (number of hours spent sitting or lying down per day) since prior studies have shown them to be associated with elevated total blood cholesterol (hypercholesterolemia). The three variables are: number of cigarettes smoked per day, number of hours they spent sitting or lying down per day, and total blood cholesterol level.

A) For our regression equation, the slope (b) =        and the intercept (a) =       .

        

B) How would you explain your regression results?

2

12

160

cigarettes 9 5 1 6 4 25 3 15 4 7 5 12 13 22 8 12 27 3 35

2

sedentariness 20 10 1 7 16 19 2 15 5 10 5 19 12 4 9 16 12 10 8

12

cholesterol 300 220 145 160 300 275 253 140 184 200 180 300 240 150 190 251 242 200 170

160

Explanation / Answer

a) The Regression equation is
y=a+bx1+cx2

From Excel

a) The regression equation is

y=150.67-0.70(cigaratees)+6.6(sedentariness)

b) If we change one unit in cigaratees then thereis 0.7 units decrease in cholestrol level.

If we change one unit in sedentariness then thereis 6.6 units increase in cholestrol level.

SUMMARY OUTPUT Regression Statistics Multiple R 0.673622 R Square 0.453767 Adjusted R Square 0.389505 Standard Error 42.19095 Observations 20 ANOVA df SS MS F Significance F Regression 2 25138.7 12569.35 7.061131 0.005857 Residual 17 30261.3 1780.076 Total 19 55400 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 150.6674 21.61542 6.970367 2.26E-06 105.0629 196.272 105.0629 196.272 cigarettes -0.70159 1.052068 -0.66687 0.513806 -2.92126 1.518078 -2.92126 1.518078 sedentariness 6.601879 1.760013 3.751039 0.001591 2.888576 10.31518 2.888576 10.31518

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