A Multiple Regression Was Performed on a Sample of 16 $\hat { y }$

question 90

Essay

A multiple regression was performed on a sample of 16 observations.The estimated equation is $\hat { y }$ = 23.5 - 14.28x₁ + 6.72x₂ + 15.68x₃.The standard errors for the coefficients are sb₁ = 4.2, sb₂ = 5.6, and sb₃ = 2.8.For this model, SST = 3809.6 and SSR = 3285.4.
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a.
Compute the appropriate t ratios.
b.
Test for the significance of β₁, β₂, and β₃ at the 5% level of significance.
c.
Do you think any of the variables should be dropped from the model? Explain.
d.
Compute R² and $R _ { \mathrm { a } } ^ { 2 }$ . Interpret R².
e.
Test the significance of the relationship among the variables at the 5% level of significance.

Recognize the challenges and benefits associated with fostering cultural diversity within organizations.

Understand the relationship between entrepreneurial culture and characteristics like risk-taking, creativity, and growth.

Grasp the concept of organizational dissent and its implications within the workplace.

Identify and describe the anatomy of the human respiratory system.

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Definitions:

Independent Variables

Elements in a research or modeling scenario that are deliberately modified to examine their influence on variables that are affected by them.

Stepwise Regression

A method of regression analysis that involves adding or removing predictors based on their statistical significance in a step-by-step manner to identify a model with optimal predictors.

P-values

A measure in statistical hypothesis tests representing the probability of observing the given or more extreme results assuming the null hypothesis is true.

Stepwise Regression

Stepwise regression is a statistical method of building predictive models by sequentially adding or removing variables based solely on their statistical significance.