2.3-2.4 solutions

If rainfall increases by 1 inch how much do you

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10. If rainfall increases by 1 inch, how much do you predict corn production will change by? a. 89.543 bushels per acre b. 0.128 bushels per acre c. 0.608 bushels per acre d. None of the above or can’t tell without more information 11. How well does this slope do at making a good prediction about the change in corn production for each additional inch of rain? Only moderately well since r is 0.608. Suppose that the price (in $thousands) and size (in square feet) of a random sample of houses in Viroqua, Wisconsin was analyzed by a new statistician using Minitab. The group plans to us the data to help set prices for homes based on their size. Descriptive Statistics: Size Variable N N* Mean SE Mean StDev Variance Minimum Q1 Median Q3 Size 10 0 1993 110 349 121907 1526 1699 1957 2271 Variable Maximum Size 2595 Descriptive Statistics: Price Variable N N* Mean SE Mean StDev Variance Minimum Q1 Median Price 10 0 219.1 19.0 60.1 3612.1 148.0 163.5 200.5 Variable Q3 Maximum Price 269.8 315.0 Correlation: 0.9041 Regression Analysis Predictor Coef SE Coef T P-value Constant -90.88 52.62 -1.73 0.12 Size 0.15556 0.02605 5.97 0.00 2
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12. True or False: Because there is a minus sign on 90.88, that means the slope of the best fitting line here is negative. False; this is the sign on the Y-intercept, not the sign for slope. 13. 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? a. Price on X axis, Size on Y axis b. Size on X axis, Price on Y axis c. It doesn’t matter. The regression line won’t change if you switched X and Y d. “Size” variable on the X axis and “Constant” variable on the Y axis 14. What is the equation of the best-fitting regression line? Find this in two ways. First, using the regression analysis part of the output, and then using the descriptive statistics part of the output. Equation either way should be Price (in thousands) = -90.88 + 0.156 Size (in sq feet) 15. For each square foot increase in house size, how much does the price increase (in dollars) on average? Explain your answer. 0.156 is the slope, which is change in price (thousands) per one more square foot of house. So one more square foot costs 0.156 thousand dollars. Or, one more square foot costs 0.156 x 1,000 = 156 dollar increase in price. 16. Does the Y-intercept have an interpretation here? Why or why not? No since you also would never have a house with X = 0 square feet, so you wouldn’t plug X=0 into this equation and expect to interpret Y. (Which is a good thing because the Y-intercept turns out to be -90.88 which you cannot interpret in this problem.) Let x be the change in a stock market index in January and let y be the change in the stock market index for the entire year. Descriptive statistics from 1960 to 1997 are shown below. Descriptive Statistics: Jan, Year Total Variable Count Mean StDev Minimum Median Maximum Jan 37 0.018 0.016 0.002 0.020 0.200 Year 37 0.091 0.010 0.520 0.101 0.393 Pearson correlation of Jan and Year = 0.796 P-Value = 0.895 17. You want to use the January change in stock market index (x) to predict the change in the stock market index for the entire year (y). Find the equation of the best-fitting line.
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