Multiple Regression Analysis Was Used to Study the Relationship Between $\beta$

question 73

Essay

Multiple regression analysis was used to study the relationship between a dependent variable, y, and three independent variables x₁, x₂ and, x₃. The following is a partial result of the regression analysis involving 20 observations.
a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not $\beta$ ₁ is significantly different from zero ( $\alpha$ = 0.05).
c.Perform a t test and determine whether or not $\beta$ ₂ is significantly different from zero ( $\alpha$ = 0.05).
d.Perform a t test and determine whether or not $\beta$ ₃ is significantly different from zero ( $\alpha$ = 0.05).
e.At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.

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Definitions:

Samples

Individual observations or subsets of data collected from a larger population for the purpose of statistical analysis.

Balanced Experiment

An experimental design where all groups or treatments have an equal number of subjects, minimizing bias and variability.

Factorial Experiment

An experimental setup that studies the effects of two or more factors across multiple levels for each factor.

College Graduates

Individuals who have completed a degree program at a college or university.