The effect of manganese (Mn) on wheat growth is examined in the article ?Manganese Deficiency and Toxicity Effects on Growth, Development and Nutrient Composition in Wheat? (Agronomy Journal [1984]: 213? 217). A quadratic regression model was used to relate y ?plant height (cm) to x ?log (added Mn), with ?M as the units for added Mn. The accompanying data were read from a scatterplot in the article. Also given is Minitab output, where x₁ = x and x₂= ?x². Use a .05 significance level for any hypothesis tests needed to answer the questions that follow.

a. Is the quadratic model useful for describing the relationship between y and x?

b. Are both the linear and quadratic predictors important? Could either one be eliminated from the model? Explain.

c. Give a 95% confidence interval for the mean y value when x = 2. The estimated standard deviation of a + b₁ (2)+ b₂ (4) is 1.037. Interpret the resulting interval.

d. Estimate the mean height for wheat treated with 10 mM of Mn using a 90% interval. (Note: The estimated standard deviation of a + b₁ (1)+ b₂ (1) is 1.031 and log(10) = 1.)

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x -1 -4 0 .2 1 2 2.8 3.2 3.4 37 44 45 46 42 4 y 32 42 40 37 30 The regression equation is Y = 41.7 + 6.58X1 - 2.36X2 Predictor Coef Stdev t-ratio Constant 41.7422 0.8522 48.98 X1 6.581 1.002 6.57 -2 p621 R-sq = 89.8% X2 0.3073 -7.69 S= 1.963 Analysis of Variance R-sq(adj) = 86.9% SOURCE DF MS Regression 2 237.520 118.760 Error 7 26.980 3.854 Total 9 264.500 x -1 -4 0 .2 1 2 2.8 3.2 3.4 37 44 45 46 42 4 y 32 42 40 37 30 The regression equation is Y = 41.7 + 6.58X1 - 2.36X2 Predictor Coef Stdev t-ratio Constant 41.7422 0.8522 48.98 X1 6.581 1.002 6.57 -2 p621 R-sq = 89.8% X2 0.3073 -7.69 S= 1.963 Analysis of Variance R-sq(adj) = 86.9% SOURCE DF MS Regression 2 237.520 118.760 Error 7 26.980 3.854 Total 9 264.500

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A quadratic regression model was used to relate to y plant height cm x log a... View the full answer