The strength of paper used in the manufacture of cardboard boxes (y) is related to the percentage of hardwood concentration in the original pulp (x). Under controlled conditions, a pilot plant manufactures 16 samples, each from a different batch of pulp, and measures the tensile strength. The data that follow will be used to answer all questions on this assessment. 101. 117 117. 106. 4 4 2 5 5 131. 146. 146. 133 2 2 2 2 2 4 111. 123. 25 45 0 0 2 2. 5 134. 144. 143. 146. S 3. 3. 5. 1. (10 points) Fit a simple linear regression model to the data. 2. (10 points) Test for significance of regression using a = 0.05, calculate the P-value, and provide an interpretation of your findings. 3. (10 points) Construct a 90% confidence interval on the slope B,.4. (10 points) Construct a 95% confidence interval on the mean strength at x = 2.5. 5. (10 points) Sketch a graph of the residuals and comment on model adequacy