Assignment 2.3-2.4

# 25 suppose you want to use the husbands age to

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*25. Suppose you want to use the husband’s age to predict the woman’s age. Find the slope of the regression line. Suppose a manufacturer has recorded its cost of electricity (in dollars) and the total number of hours of machine time for their factory during a certain number of weeks. They want to use the data to estimate electric bills based on machine time. Their new statistician analyzed the data. The results are shown below. Descriptive Statistics: Time, Cost Variable N Mean SE Mean StDev Variance Minimum Q1 Median Time 52 10.865 0.369 2.664 7.099 6.000 8.000 11.000 Cost 52 1041.9 35.9 258.9 67043.1 464.3 879.2 1018.8 Variable Q3 Maximum Time 13.000 15.000 Cost 1243.2 1598.1 Pearson’s Correlation: 0.7375 26. Based on the above output, a scatterplot of this data set that will be used for prediction purposes would have which variable on which axis? 27. Interpret the correlation in the context of this problem. What additional variables might be related to electric bills besides hours of machine time? 28. What is the equation of the best-fitting regression line? Justify your answer. 29. How many weeks of data were included in this study? 30. For each additional hour of machine time, how much does the cost increase (in dollars) on average?

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31. For what machine times would you feel comfortable using your best fitting regression line to make predictions about electricity cost? Use the statistical information given in the problem to answer. 32. What is the Y-intercept in this problem? Can it be interpreted in the context of this problem? If yes, interpret it. If no, explain why not. Suppose the increase in blood pressure (Y) is estimated by dosage of a drug (X mg). The equation of the best fitting regression line is Y = 0.05X. The correlation was found to be +0.80 *33. If the dosage increases by 10 mg how many units is BP expected to increase by? 34. Explain why the Y-intercept should be 0 for this problem. A jeweler in Singapore advertises the prices of 48 diamonds in her showroom. You record the weight of each diamond, along with the price, to see whether you can predict price using weight. The analysis is shown below. Weight is measured in carats (1 carat = .2 grams). Price is measured in Singapore dollars. (Note: some numbers have been replaced with question marks.) Descriptive Statistics: Weight, Price Total Variable Count Mean St Dev Minimum Q1 Median Q3 Maximum Weight 48 0.20417 ???? 0.12000 0.16000 0.18000 0.25000 0.35000 Price 48 500.1 213.64 223.0 336.5 428.5 661.0 1086.0 Predictor Coef SE Coef T P Constant -259.63 17.32 -14.99 0.000 Weight 3721.02 81.79 45.50 0.000 Pearson’s Correlation: 0.959. 35. Which of the statements below describes the correlation for this problem? a. As weight increases, price tends to also increase. b. There is a strong positive linear relationship between weight and price.
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