A Researcher Wanted to Study Effect of Two Factors, X₁

question 40

Essay

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below.
a. Develop an estimated regression equation with both factors x₁ and x₂ as the independent variables. Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters?
b. How much of the variation in the sample values of y does the model in part (a) explain?

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Definitions:

Directional Hypothesis

A hypothesis that specifies the direction of the expected difference or relationship between two variables.

Critical Value

A threshold in hypothesis testing that determines the boundary for rejecting or failing to reject the null hypothesis.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis; it marks the threshold of statistical significance.

P Value

The probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is correct.