A sample of n = 20 hospitals was selected, and the values of y = monthly labor-hours and k = 15 workload variables (items that result in need for personnel in a hospital such as X- ray exposures and length of patient's stay) were determined. The goal here is to produce a regression equation that will estimate (or predict) personnel needs for hospitals. When the multiple regression model using these 15 predictors was fit to the data, R = 0.94 resulted. (1) Does the model appear to specify a useful relationship between y and the predictor variables? Carry out a test using significance level 0.05. [Hint: State the hypotheses, calculate the F ratio, compare to the F critical value, draw conclusion.] (2) Based on the result of part (1), does a high R2 value by itself imply that a model is useful? Under what circumstances might you be suspicious of a model with a high R value? (3) Calculate Rdj (4) After deleting 12 variables, we fit the model with just 3 predictors I = monthly X-ray exposures, r2 = monthly occupied bed-days, 13 = average length of patient's stay, in days. The estimated regression equation is ý = 2000 + 0.03.r1 +1.08r2- 440r3 R remains the same. In addition, MSE = 100,000, the estimated standard error of Bi is 0.012. Calculate and interpret a 90% CI for B1. (5) Using the model from (4), a 95% CI for the true average monthly labor-hours when a = 1000, r2 = 500, and r3 4 is calculated to be [492, 1128]. Compute a 95% PI for the monthly labor-hours of a new hospital with r = 1000, r2 = 500, and ra = 4.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.