Stat2Lab8

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Stat 2 Lab #8: Regression – Roadmap, Regression Effect, and RMS Error Learning objectives: • Use residual plots to check assumptions underlying regression • Define and calculate the RMS error for regression and the RMS error • Carry out normal approximations for a given value of x in regression, using the appropriate average and standard deviation (“slice problems”) • Explain and apply the regression effect Part 1. (Starting with the same data as last lab….) A realtor collects data about the rental prices of apartments in a neighborhood and their size measured in square feet. They find that the apartments have an average size of 1000 square feet, with a standard deviation of 300 square feet. The apartments have an average rental price of $1500 per month, with a standard deviation of $400. The two variables have a correlation of r = 0.5. A scatterplot of the two variables looks football shaped. 1. Recall that last time we found the following predictions of price based on size: 1000 square feet: predicted price = $1500 700 square feet: predicted price = $1300 1600 square feet: predicted price = $1900 The above predictions all are subject to error. The average size of such errors is about $__________, and 95% of the predictions we make using regression will be correct to within about $__________. If we predicted rental price without taking size into account, the average size of the errors would be $__________, and 95% of the predictions we make using regression will be correct to within about $__________. Emily Gimenez 346 . 41 692 . 82 400 SOU - SDOfY 1 - r2 TF0 . 5 400 = $ 346 41

2. An apartment is at the 25 th percentile in terms of area. Use regression to predict what its percentile rank will be in terms of price. (Hint: This is similar to what you did in #6 and #7 in the last lab, but starting with percentile rank for x rather than x in original units, and without prompting you for the intermediate steps. Look at the roadmap.)

Part 2. 3. City planners compile data on buildings in a city. For each building, they record the number of stories (floors) as well as the height of the building in feet. The number of stories has an average of 30 stories, with an SD of 15 stories. The height has an average of 400 feet with an SD of 90 feet. The correlation is strong but not perfect, with r = 0.8. A scatterplot with stories on the horizontal axis and height on the vertical axis is football shaped. (a) For each variable, circle all the terms that are applicable. Stories (floors): quantitative qualitative discrete continuous Height: quantitative qualitative discrete continuous (b) About what percent of all the buildings are more than 500 feet tall? _____________% (c) About what percent of buildings with 50 stories are over 500 feet tall? ____________%

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4. The freshmen at a large university are required to take a battery of aptitude tests. Students who score high on the mathematics test also tend to score high on the physics test. On both tests, the average score is 60; the SDs are the same too. The scatter diagram is football-shaped. Of the students who scored about 75 on the mathematics test: (i) Just about half scored over 75 on the physics test (ii) More than half scored over 75 on the physics test (iii) Less than half scored over 75 of the physics test Choose one option and explain. It will help to draw a picture.

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