Microsoft Word - M15Chap13Homework.docx Math 15 Homework Assignment Read sections 13.7 – 13.10 1. The article “Crop Improvement for Tropical and Subtropical Australia: Designing Plants for Difficult...

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Microsoft Word - M15Chap13Homework.docx Math 15 Homework Assignment Read sections 13.7 – 13.10 1. The article “Crop Improvement for Tropical and Subtropical Australia: Designing Plants for Difficult Climates” (Field Crops Research, 1991) gave the accompanying data on x = crop duration in days for soybeans and y = crop yield in tons/hectare.     (a) Draw a scatterplot of the raw data and a residual plot. Give interpretations of both. (b) Conduct a hypothesis test for β. Give the p-value and statement about whether the linear relationship is statistically significant. (c) Identify any outliers and describe the effect they may have on the analysis. (d) Give an explanation of the coefficient of determination. (e) Give a 95% prediction interval estimate for the crop yield corresponding to a crop duration of 105 days.   2. The PJH&D Company is in the process of deciding whether to purchase a maintenance contract for its new word-processing system. The company feels that maintenance expense should be related to usage, and it has collected the following information on weekly usage (hours) and annual maintenance expense:     (a) Sketch the scatterplot for regressing y on x . Be sure to label your axes and circle on your plot Observation #4. (b) Find the equation of the least squares regression line for regression y on x. (c) Draw (or superimpose) the regression line in part (b) on the scatterplot in part (a). (d) Suppose that the weekly usage for a company is 21 hours. Predict their annual maintenance expense. Show your work and include your units. (e) Using the new word-processing system incurs other expenses besides maintenance costs. Suppose that weekly utility costs, C , in dollars, is related to weekly usage by the following equation: C = 3 X - 0.80. What would be the correlation between weekly utility cost, C , and annual maintenance cost, Y? (f) Sketch the residual plot on the basis of this regression analysis. Be sure to label your axes and circle on your plot the residual for Observation #4. (g) Based on the residual plot, does the linear model seem appropriate? Explain.