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 101.4 117.4 117.1 106.2 1.0 1.5 1.5 1.5 131.9 146.9 146.8 133.9 X 2.0 2.0 2.2 2.4 y 111.0 123.0 125.1 145.2 X 2.5 2.5 2.8 2.8 V 134.3 144.5 143.7 146.9 3.0 3.0 3.2 3.3 O 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 Bi. 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