STAT
2.3-2.4 solutions

# They are using machine time to estimate the cost so x

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They are using machine time to estimate the cost, so X = machine time and Y = cost. 27. Interpret the correlation in the context of this problem. What additional variables might be related to electric bills besides hours of machine time? The correlation is .7375 which is moderate, positive, and linear(assuming we looked at the scatterplot). This means as time goes up, electricity does too, in a moderately predictable linear pattern. Other variables might include power needed for each machine, etc. 5

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28. What is the equation of the best-fitting regression line? Justify your answer. Slope = = 71.67 Y-intercept = =263.21 Cost = 263.21 + 71.67 (hours of machine time) 29. How many weeks of data were included in this study? 52 30. For each additional hour of machine time, how much does the cost increase (in dollars) on average? 71.67 dollars 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. 6 (minimum time in the data set) to 15 (maximum time in the data set) 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. \$263.21 dollars in electric costs for 0 hours machine time. You could describe this as fixed cost before the machines are being used. But since time for this data set started at 6 hours so we can’t make a close prediction here with confidence. 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? 0.05 * 10 = .5 units of BP increase 34. Explain why the Y-intercept should be 0 for this problem. there is no increase to measure yet since there is no drug given. 6
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 weight using price. 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. c. You can use weight to predict price using a regression line and it would fit well. d. All of the above.

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