Question 7. A researcher is interested in investigating whether net revenues of
ID: 3334780 • Letter: Q
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Question 7. A researcher is interested in investigating whether net revenues of health care facilities are different between rural and non-rural facilities. Data are collected from 52 licensed facilities as follows Y Net revenue ($10,000 unit) X Indicator variable (1 if rural facility and 0 if non-rural facility) X Number of beds in facility Annual medical in-patient davs Annual total patient days Th l y= +Bx, +-X, + , x, t 4X, + is fitted and e linear regressionmode the output is given as follows:Explanation / Answer
1. with a unit increase in x2 there is 0.17 units increase in y
ho: beta_2 is not significant. v/s h1: beta_2 is significant
with t = (.17/.19)= 0.8947 and p-value 0.3752 (T.DIST.2T(0.894737,50)) being greater than alpha, I reject ho and conclude that beta2 Is not significant
2. ho: model is not significant. v/s h1: model is significant. With F = 42.64 and p-value (0.00) being less than alpha, I reject ho and conclude that model is significant.
source
SS
Df
MS
F
regression
121255
=4-1
=121255/3
=40418.33/947.729
residual
45491
=51-3
=45491/48
total
=121255+45491
51
=166746/51
source
SS
Df
MS
F
regression
121255
3
40418.33
42.64756
residual
45491
48
947.7292
total
166746
51
3269.529
3. R^2 = SSR/SST = 121255/166746 = 72.71%
this implies 72.71% variation in dependent variable is explained by independent variable x1,x2,x3 and x4
4. regression equation: y = -47.92 + 8.45*x1 + 0.17*x2 + 0.02*x3 + 0.35*x4
source
SS
Df
MS
F
regression
121255
=4-1
=121255/3
=40418.33/947.729
residual
45491
=51-3
=45491/48
total
=121255+45491
51
=166746/51
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