invest_3ed.pdf

# B joy montoya a 43 year old female did not appear in

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(b) Joy Montoya, a 43-year-old female, did not appear in the first set of results. Use these data to predict her finishing time. (c) How do the intervals in (a) and (b) compare Midpoint? Width? Explain why each has changed (or not) the way it has. (d) Repeat (b) and (c) for Laure James, a 53-year-old female who also didn’t appear in the original results. (e) Do you consider the above interval calculations to be valid? (Examine and discuss residual plots.)

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Chance/Rossman, 2015 ISCAM III Investigation 5.14 398 Investigation 5.14: Housing Prices A group of students wanted to investigate which factors influence the price of a house (Koester, Davis, and Ross, 2003). They used , limiting their search to single family homes in California. They collected a stratified sample by stratifying on three different regions in CA (northern, southern, and central), and then randomly selecting a sample from within each strata. They decided to focus on homes that were less than 5000 square feet and sold for less than \$1.5 million. The file housing.txt contains data for their final sample of 83 houses. Below is a scatterplot of the size vs. selling price for this sample. (a) Open the housing file and determine the least-squares regression line for these data. Also report and interpret the value of r 2 for these data. (b) Based on the scatterplot, do these data appear to fit the basic linear regression model? (c) Produce a histogram and a normal probability plot of the residuals of this regression. Is it reasonable to consider the residuals as following the normal distribution? Explain. (d) Produce a scatterplot of the residuals vs. the square footage. Does there appear to be curvature in this graph? Does the variability in the residuals appear to be roughly constant across the graph?
Chance/Rossman, 2015 ISCAM III Investigation 5.14 399 Discussion : It takes a while to become comfortable interpreting these residual plots, but the housing data do appear to have some problems. The residuals appear to cluster closer to zero for the smaller houses and to have more variability for the larger houses. This violates the condition of a constant standard deviation for each value of x . There is also a very slight hint of some curvature in this graph. The distribution of the residuals is clearly non-normal. This residual analysis gives us several reasons to not apply the basic regression model to these data. When the regression model conditions are violated, we can often transform the data in the hopes that the new variables do meet the conditions. (e) Take the log base 10 of both the house prices and sizes, storing the results as logprice and logsqft . [ Hint : In Minitab, use Calc > Calculator or the let command. Also keep in mind that both R and Minitab assume natural log when use the “log” function. In Minitab use “logten” and in R use “log10”.] Produce the scatterplot and determine the regression equation to model the relationship between these two variables, storing the residuals. Examine the residual plots (histogram of residuals and residuals versus explanatory variable).

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