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

question 40

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:

Standard Error

A statistical measure of the precision for a series of measurements or the estimate of the standard deviation of the sampling distribution of a statistic.

Population Standard Deviation

A measure of the dispersion or variance in a population dataset, indicating how spread out the data points are from the population mean.

Sample Size

The number of observations or units included in a sample taken from a population for the purpose of statistical analysis.

Observed Z Value

A statistical measurement representing the number of standard deviations a data point is from the mean of a set of data.