In order to study the relation of weight to blood sugar level, medical researche

Question

In order to study the relation of weight to blood sugar level, medical researchers considered a random sample of 12 patients. The observed Pearson correlation between weight and blood sugar level was 0.63.

The researchers in the previous problem fit a simple linear regression model to the same data with blood sugar level as the response (Y) and weight as the regressor (X).

If x-165, Y = 106, Sx = 10 and S-20, compute the least squares estimates of intercept and slope. Suppose the estimated standard error of the slope. a) b) is 0.4912, construct a 99% confidence interval for

Explanation / Answer

a)here estimate value of slope b1=r*Sy/Sx =0.63*(20/10)=1.26

and  estimate value of intercept =bo =Ybar -b1*Xbar =106-1.26*165 = -101.9

b)

for (n-2=10) degrees of freedom and 99% confidence interval ; critical value of t =3.1693

therefore 99% confidence inrterval of slope=extimated value of slope -/+ t*std error

= -0.2967 to 2.8167

please revert for any explanation required.

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