Question

This preamble applied to questions 1 & 2 (Based loosely on textbook page 442) Say we are interested in examining the linear relationship between the monthly labour hours required in a hospital (y), the monthly x-ray exposures (x1), monthly occupied bed days (x2), and average length of stay (x3). We gather 10 observations, and input the data into Excel. We obtain the following output Intercept X Variable 1 X Variable 2 X Variable 3 Coefficients 1134.56 0.16 0.27 -147.93 Standard Error 221.49 0.03 0.12 39.53 t Star 5.12 5.30 2.26 -3.74 Based on this output, select the appropriate fitted regression equation (equation of the fitted regression line) Selected Answer: D=-1134.56 -0.16x7 -0.27x2 + 147.93X3 Answers: D=1134.56+0.16x2 +0.27x2 - 147.93X3 D=1134.56x2 +0.16x2 +0.27X3 - 147.93x4 ♡ = 1134.56 +0.16X1 D--1134.56 -0.16X1-0.27X2 + 147.93X3

Answer 1

Q1) From the coefficient column of the variables significance table, we have the regression equation here as:

$\hat y = 1134.56 + 0.16x_1 + 0.27x_2 - 147.93 x_3$

This is the required regression equation here.

Q2) For x₃, we can see from the coefficient table here, the test statistic as:

t = -3.74. Therefore -3.74 is the test statistic value here.

Q3) Using the given values of independent variables here, the estimated value of the dependent variable here is computed as:

9 = 200 +0.121+0.222 - 0.933

$\hat y = 200 + 0.1*100 + 0.2*50 - 0.93*200 = 34$

therefore 34 is the required predicted value here.

Q4) Here, we are given that x₂ =1 for a mechanical repair, and 0 otherwise. As the coefficient for x₂ in the table is -1.263, therefore we can conclude here that on an average a mechanical repair will take 1.263 hours less than an electrical repair. Therefore b is the correct answer here.