invest_3ed.pdf

# Usa today wloszczyna debarros investigated this by

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USA Today (Wloszczyna & DeBarros, Feb. 25, 2004) investigated this by determining a rating score for movies released in 2003 based on a compilation of movie reviews published in 20 major newspapers and magazines for over 300 movies. The movies03.txt data file contains these scores and how much money the movie made at the box office, in millions of dollars. A high composite score indicates that most critics loved the movie, and a low score indicates that most critics panned the movie. (a) Identify the observational units in this study. Also identify the explanatory and response variables, and classify them as categorical or quantitative. Observational units: Explanatory: Response: (b) Produce a scatterplot to determine whether the critic scores appear to help predict the box office gross. Describe the relationship between the two variables as exhibited in the scatterplot. (c) Identify the two or three points that you believe have the largest (in absolute value) residuals. Identify these movies by name x In R: You can use a command like > movies03[score > 90 & box.office > 250, ] x In Minitab: Use the “brush” feature: Editor > Brush , and then Editor > Set ID variables What does it mean for these movies to have such large residuals?

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Chance/Rossman, 2015 ISCAM III Investigation 5.9 379 (d) Determine, report, and interpret the value of the correlation coefficient. (e) Use technology to determine the least squares regression line for predicting the box office gross from the composite critics’ score. Report the equation for th is line. Also interpret the slope and intercept of this line in context. Equation of line: Interpretation of slope: Interpretation of intercept: (f) Report the value of r 2 and s provide interpretations in this context. Technology Detour Creating a Coded Scatterplot with Separate Lines In R x Create the coded scatterplot: > plot(box.office~score, col=rating) x Add the separate lines for each category, e.g.,: > abline(lm(box.office[rating=="G"]~score[rating=="G"])) To cycle through the categories, create a column for the four categories and create a loop: > code=c("G", "PG", "PG-13", "R") > for (i in 1:4){ abline(lm(box.office[rating==code[i]]~score[rating==code[i]]), col=i) } To add a legend: > legend("topleft", legend=code, col=1:4, pch=1) In Minitab x Choose Graph > Scatterplot and choose the With Groups option. x Enter the box office values and the ratings for the movies as before. x In the Categorical variables box enter the “rating” variable (PG -13 etc.) and then click the box next to “X - Y pairs from groups.” The resulting scatterplot should have the movies coded by rating. x Right click on the scatterplot and choose Add > Regression Fit . Check the box to Apply same groups … . Click OK .
Chance/Rossman, 2015 ISCAM III Investigation 5.9 380 (g) Describe what this coded scatterplot reveals about whether the relationship between box office income and critic scores differs across the various rating categories. In particular, does any rating category tend to have higher box office values than you would expect for the score they received from the critics? Is there a rating category tending toward lower box office revenues than expected? Explain.

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