To help schedule staffing and equipment needs, a large hospital uses a multiple regression model to predict its 'bed census' y , the number of beds occupied at the end of each day. Using hospital records from the most recent 27 days, a total of 3 independent variables are used to find the estimated regression model. Let β1 , β2 , and β3 denote the coefficients of the 3 variables in this model. A computer printout indicates that the total sum of squares (SST) associated with the model is 710.26 and the corresponding regression sum of squares (SSR) is 305.30 . Using a significance level of 0.05 , can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily bed census? Perform a one-tailed test. The null hypothesis: H0: The alternative hypothesis: H1 : at least one of the independent variables is useful The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least two decimal places.) The critical value at the 0.05 level of significance:(Round to at least two decimal places.) Can you conclude that at least one of the independent variables in the model provides useful information for predicting daily bed census? Yes No
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
To help schedule staffing and equipment needs, a large hospital uses a multiple regression model to predict its 'bed census'
, the number of beds occupied at the end of each day. Using hospital records from the most recent
days, a total of
independent variables are used to find the estimated regression model. Let
,
, and
denote the coefficients of the
variables in this model. A computer printout indicates that the total sum of squares (SST) associated with the model is
and the corresponding regression sum of squares (SSR) is
. Using a significance level of
, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily bed census?
Perform a one-tailed test.
| The null hypothesis: |
H0:
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| The alternative hypothesis: | H1 : at least one of the independent variables is useful | |||
| The type of test statistic: | (Choose one)ZtChi squareF | |||
| The value of the test statistic: (Round to at least two decimal places.) |
|
|||
| The critical value at the 0.05 level of significance: (Round to at least two decimal places.) |
|
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| Can you conclude that at least one of the independent variables in the model provides useful information for predicting daily bed census? |
|
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