A toy manufacturing company produces a plastic material which is used in the manufacture of toys. The company's quality control department has conducted a study to determine the extent to which the tensile strength (in kg / cm²) of this plastic could be affected by the thickness of the material as well as its density. Twelve tests were carried out and the results are shown in the table below.

1. (2 pts) What percentage of variation in tensile strength is explained by each of the regressions? Complete the following Table:

3. (2 pts) Complete the following analysis of variance table for the regression comprising the two independent variables.

4. (3 pts) We would like to test the significance of the regression by considering the nullhypothesis Ho: P₁ = B₂: = 0. State the alternative hypothesis and conduct the test at5% significance level. What doyou conclude? 5. (2 pts) In the case of the linear model that comprises only the thickness as a regressor,determine a 95% confidence interval for B₁. 6. (2 pts) With the confidence interval calculated in question 5., can we say, at 5%significance level, that the linear regression is significant between the tensile strengthand material thickness? Justify your conclusion. 7. (2) Quantify the marginal contribution of the variable x2 when it is introduced after thevariable x₁?