A First-Order Model Was Used in Regression Analysis Involving 25

question 62

Essay

A first-order model was used in regression analysis involving 25 observations to study the relationship between a dependent variable y and three independent variables x₁,x₂,and x₃.The analysis showed that the mean squares for regression is 160 and the sum of squares for error is 1050.In addition,the following is a partial computer printout.
a.Develop the ANOVA table.
b.Is there enough evidence at the 5% significance level to conclude that the model is useful in predicting the value of y?
c.Test at the 5% significance level to determine whether x₁ is linearly related to y.
d.Is there sufficient evidence at the 5% significance level to indicate that x₂ is negatively linearly related to y?
e.Is there sufficient evidence at the 5% significance level to indicate that x₃ is positively linearly related to y?

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Definitions:

Rational Decisions

Choices made by individuals that align with their own self-interest and are based on an evaluation of the costs and benefits of the action.

Marginal Costs

The extra financial burden of generating one additional unit of a good or service.

Marginal Benefits

The incremental satisfaction or advantage obtained from the consumption of an additional unit of a good or service.

Marginal Cost

Marginal cost is the increase in total production cost that arises from producing one additional unit of a good or service.