please show all steps in details especially for hypothesis testing

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Problem 1 140 pts Caulkins, J.P. and R. Padman (1993) in their paper on the quantity discounts and quality premia for illicit drugs aim to estimate the effect of quantity, quality and trend on the price of drugs in California. The data contains 56 observations and covers the below variables: PR = price per gram in dollars for a drug sale QUT=number of grams of drugs in a given sale QUL = quality of the drug (in percentage purity) - TRE = time variable with 1984=1 to 1991=8 The regression model is given by PR = Bo + B.QUT + B2QUL + B3TR +e (a) What would you expect the signs of the coefficients B1,B2 and 33 to be? Why? [5 pts) (b) The estimated equation is PR = 90.8467 + -0.06QUT + 0.1162QUL - 2.3546 TR R2 = 0.50971 (se) (8.5803) (0.0102) (0.2033) (1.3861) (t) (10.588) (-5.892) (0.5717) (-1.6987) i. Interpret the coefficient estimates. [5 pts] ii. What proportion of the variation in drug price is explained jointly by variation in quantity, quality and trend? (5 pts) It is argued that the greater the number of sales, the higher the risk of getting caught. Therefore, sellers are willing to accept lower price if they can make sales in larger quantities. What would H, and Hbe? Carry out the hypothesis test. [10 pts) iv. Test the hypothesis that the quality of drugs has no influence on price against the alternative that a premium is paid for better-quality drugs. [10 pts) Construct a 95% confidence interval for B2? (5 pts] V