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. y 101 117. 117. 106. 4 4 2 1.0 1.5 1.5 131. 146 146 133 O 8 2.0 2.0 2.2 2.4 111. 123 125. 145 0 2.5 2.5 2.8 2.8 134. 144. 143 146. 3 5 3.0 3.0 3.2 3.3 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,.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