6.5. Extension of steel wires Ten steel wires of diameter 0.5 mm and length 2.5 m were extended in a laboratory by applying vertical forces of varying magnitudes. Results are as follows 19 25 35 48 53 Force, kg Increase in length, mm 62 6.6 15 42 3.9 56 65 1.7 2.1 2.5 3.4 4.9 5.4 5.7 7.2 (1) Estimate the parameters of a simple linear regression model with force as the explanatory variable (2) Find 95 percent confidence limits for the two parameters (3) Test the hypothesis that the intercept is zero (4) What are the conclusions?

Suppose you are given a Rectangular piece of cardboard having length 3x-7 inches and width 5x+2 inches. Then you cut out a square from this piece of cardboard having side length x inches. Find the area of the remaining piece of cardboard expressed in terms of x. Please provide steps in detail and how you are thinking to get to a solution.  Thank you