Question

A surgical practice reported the results of a regression analysis, designed to predict the monthly income the surgeons bring into the practice (Y) – measured in thousands of dollars. One independent variable used to predict monthly income for the surgical practice is the number of new patients (X) enrolled by each surgeon. The firm samples 12 surgeons and determines for each the number of new patients they have enrolled monthly and the amount in thousands of dollars they have brought into the practice. The data were used to fit a linear model. The results of the simple linear regression are provided below.

        Y = 17.7 + 1.12X; S_YX =$5.804; 2 – tailed p value = 0.000126 (for testing ß₁);                

                       S_b1=0.185;    X = 25.083; SSX=Σ( X_i –X )²=980.917;   n=12 ;

         Interpret the Y intercept estimate of the line. what can be inferred and makes the most sense out of the following four choices:

   

		The Y intercept is not explained by regressing monthly income on new patients.
		For every $1 thousand increase in firm income, we expect 17.7 new patients.
		About 95% of the observed monthly income fall within 17.7 of the line of regression.
		Surgeons will bring into the firm at least $17.7 thousands monthly.

Answer 1

Correct option is:

Surgeons will bring into the firm at least $17.7 thousands monthly.

(since y intercept is monthly income when 0 patient added)