3. There are plenty of hypothesis tests associated with any set of regression results. Here's one set of results from a regression of Y, crop output per acre, on F, pounds of fertilizer per acre. Call: lm(formula = Y ~ F) Residuals: Min 10 Median 3Q Max 4.4497 -10.0635 -1.3642 0.5394 1.8302 Coefficients: Estimate Std. Error t value Pr (>1t|) (Intercept) 1.225e+02 1.042e+00 117.5682e-16 *** 6.997e-02 8.912e-03 7.852 2.98e-13 *** F --- Signif. codes: 01*** 0.001 0.01 0.05 0.1 1 Residual standard error: 2.569 on 189 degrees of freedom Multiple R-squared: 0.246, Adjusted R-squared: 0.242 F-statistic: 61.65 on 1 and 189 DF, p-value: 2.981e-13 Oh, pro tip, when pasting results from R Studio into a Word document, it's good to use a font like Courier that has letters and numbers that are all the same width. A. What are the values for the (Multiple) R-squared and the Adjusted R-squared and what do these mean? B. In general, what relationship is there between the size of the R-squared and the t-test about coefficients on explanatory variables? C. What are the values of the t-statistic and the associated p-value for the t-test about the coefficient on F, which is the explanatory variable here, and what do these values tell you about the estimated coefficient on F? D. What is the p-value associated with the F-test here? F also stands for "fertilizer" here, but it's also a statistical test. What does this p-value mean? E. Look at the p-value for the t-test and at the p-value for the F-test. Is this an odd coincidence, or is there a relationship between the F-test and the t-test in a linear regression model with one explanatory variable?