A Researcher Wanted to Study Effect of Two Factors, X₁

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?