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An agronomist designed a study in which tomatoes were grown using six different amounts of fertilizer: 0, 20, 40, 60, 80, and 100 pounds per 1,000 square feet. These fertilizer application rates were then randomly assigned to plots of land. The results including the yield of tomatoes (in pounds) are stored in Tomato and are listed here: SELF Test r 2 . Fertilizer Application Fertilizer Application Plot Rate Yield Plot Rate Yield 1 0 6 7 60 46 2 0 9 8 60 50 3 20 19 9 80 48 4 20 24 10 80 54 5 40 32 11 100 52 6 40 38 12 100 58 a. Construct a scatter plot for fertilizer application rate and yield. b. Fit a quadratic regression model and state the quadratic regression equation. c. Predict the yield for a plot of land fertilized with 70 pounds per 1,000 square feet. d. Perform a residual analysis on the results and determine whether the regression model is valid. e. At the 0.05 level of significance, is there a significant overall relationship between the fertilizer application rate and tomato yield? f. What is the p-value in (e)? Interpret its meaning. g. At the 0.05 level of significance, determine whether there is a significant quadratic effect. h. What is the p-value in (g)? Interpret its meaning. i. Interpret the meaning of the coefficient of multiple determination. j. Compute the adjusted r 2
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