1. Ten steel rods of nominally the same composition and diameter were subjected to various tensile forces (or, in thousands of pounds), and elongation (y, in thousands of an inch) of the steel rods was observed. The following data was observed: @121 32%- = 45.8, 2101 $3 = 260.46, 2;; yz- = 630, :10 y? = 48735.1, 231 xiyt- = 3558.42. 3: i=1 (a) Fit the least squares line that will enable us to predict elongation in terms of tensile force. For (b) and (c), assume independent normally distributed errors with mean zero and common variance. (b) Find a 99% condence interval for the expected change in elongation corresponding to a 1000 pounds increase in force (notice, that this means a unit change in x). Hint: A CI for the slope parameter is actually requested. (c) Find a 95% condence interval for the expected elongation corresponding to a force of :3" = 5 thousands of pounds. Also, nd a prediction interval for elongation corresponding to the same value of the force. Which interval is wider? Does it make sense