Multiple Regression Analysis Was Used to Study the Relationship Between

question 135

Essay

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and four independent variables; X1, X2, X3 and, X4. The following is a partial result of the regression analysis involving 31 observations.
$\begin{array}{lcc} & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 18.00 & 6.00 \\\mathrm{X}_{1} &12.00 & 8.00 \\\mathrm{X}_{2} & 24.00 & 48.00 \\\mathrm{X}_{3} &-36.00 & 36.00 \\\mathrm{X}_{4} &16.00 & 2.00\end{array}$
$\text { Analysis of Variance }$
$\begin{array}{lllc}\text { Source } & \text { DF } & \text { SS } & \text { MS } &F\\\text { Regression } & & & 125\\\text { Error }&&\\\text { Total }&&760\end{array}$
a. Compute the coefficient of determination.
b. Perform a t test and determine whether or not β₁ is significantly different from zero α = 0.05).
c. Perform a t test and determine whether or not β4 is significantly different from zero α = 0.05).
d. At α = 0.05, perform an F test and determine whether or not the regression model is significant.

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Definitions:

Nonnutritive Sweeteners

Artificial or natural sweeteners that provide little to no nutritional value but add sweetness to foods and drinks.

Total Fat Intake

The total amount of fat consumed in one's diet over a specified period.

Physical Activity

Any bodily movement produced by skeletal muscles that require energy expenditure, beneficial for health.

High-Protein Foods

Foods that are rich in protein, essential for building and repairing body tissues, and include items such as meat, fish, eggs, and beans.