A Researcher Wanted to Study Effect of Two Factors, X₁

question 53

Essay

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below. $\begin{array}{|c|c|c|c|}\hline \text { Observations } & \boldsymbol{x} \mathbf{1} & \boldsymbol{x} \mathbf{2} & \boldsymbol{y} \\\hline 1 & 42.5 & 30.1 & 260.4 \\\hline 2 & 43.5 & 29.3 & 261.7 \\\hline 3 & 43.9 & 31.1 & 273.6 \\\hline 4 & 44.8 & 29.6 & 278.6 \\\hline 5 & 46.8 & 29.7 & 281.5 \\\hline 6 & 47.5 & 29.9 & 294.6 \\\hline 7 & 50.1 & 30.1 & 301.2 \\\hline 8 & 51.9 & 30.4 & 314.6 \\\hline 9 & 54.7 & 30.5 & 320.5 \\\hline 10 & 54.8 & 31 & 324.7 \\\hline 11 & 57.1 & 31.8 & 356.7 \\\hline 12 & 57.8 & 31.4 & 370.3 \\\hline 13 & 62.3 & 31.5 & 378 \\\hline 14 & 66.7 & 32.1 & 384.8 \\\hline 15 & 71.2 & 32.5 & 396.9 \\\hline\end{array}$
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?

---

Definitions:

Two High Courts

Typically refers to the supreme judicial bodies within a dual-court system, which may handle different jurisdictions, such as constitutional matters and appellate review.

Civil Cases

Legal disputes between individuals or organizations resolved through the court system, often involving compensation rather than criminal penalties.

Criminal Cases

Legal proceedings that involve the prosecution by the state of a person or organization charged with a crime.

Improper Instructions

Instructions that are incorrect, misleading, or incomplete, potentially leading to errors or legal issues.