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Question 1:

A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period. and then their heights {in inches} were measured. A portion of the data is shown in the accompanying table. Height: Fertilizer 20.4 1.9 29.1 5.0 36.4 3.1 Click here for the Excel Data File a. Estimate the linear regression model: Height - .30 + lPartilizsr + a. {Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Ham Fem-r b-1. Estimate the quadratic regression model: Height - .30 + lFartilizer + ZFertilizarz + a. {Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Ham _l__ Fem-e b-2. Using the quadratic results, find the fertilizer amount at which the height reaches a minimum or maximum. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Fertilizer amount = ounces c. Use the best-fitting model to predict, after a four-month period, the height of a tomato plant that received 3.0 ounces of fertilizer. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Height = inchesStandard Coefficients rm: i: Stat pValua Intercept 21.13194 733.112 23.839 1.562-16 Age -1,208.25 123.95 2.41E08 a. Specify the competing hypotheses in order to determine whether the selling price of a used car and its age are linearly related. 0H0: 31 1 ; HA: J31 c [l H: .81 I U; HA: 31 l G 03.3: l 5 it, Hi: J31 3 G b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Tent statistic 3.3?!) c1. Find the p-value. pvalue O OHQ: By = 0; HA: Bj 0 O Ho: B1 = B2 = B3 = B4 = 0; HA: At least one Bj 1 OH0: B1 = 1; HA: B1 O OHO: B1 = 0; HA: B1