1. (16 points) Consider the following summary output from using statistical software to fit a simple linear regression model to a data set for which y = weight in kg and x = height in cm. Assume the subjects comprising the data are a random sample of 16-year-old girls from the 1950s. Estimate Std. Error t value Pr (>It|) (Intercept) -36.8759 64 . 4728 -0.572 0. 583 X 0 . 5821 0. 3892 1 . 496 0. 173 Residual standard error: 8.456 on 8 degrees of freedom Multiple R-squared: 0.2185, Adjusted R-squared: 0. 1208 (a) Clearly state, exactly what assumptions (about the population from which the data were drawn) are necessary for the computations summarized above to be valid and meaningful. (A precisely defined statistical model for the population distribution of X and Y would be one way to answer this question.)