AP statistics (homework help)
Graded Assignment MTH510A: AP Statistics | Unit 3 1 3.3 Practice 7 4. Below is some hypothetical data that shows the Rating (an index of how many people watch the show) and Average Cost for a 30-second advertisement for a number of game shows GAME SHOW Rating Average Cost for a 30 Is That Real Hair? Second Ad ($) 18.2 $55,000 Feng Shui Happy Booth 8.4 $20,000 Love Signals! 13.6 $26,000 How Many Worms? 11.9 $39,000 Spin the Bottle 9.0 $11,000 Wake that Possum! 22.6 $75,000 Sit on a Potato 3.5 $10,000 Name that Fruit! 2.1 $5,000 The $2.00 Question 4.6 $19,000 As before, conduct a full (five step) regressional analysis to answer this question: Within the sample data, is an increase in ratings associated with an increase the average cost for a 30-second ad? If so, how much? (5 points) 5. Demographers often examine the relationship between income measures and population factors such as births, deaths, marriages, or migration rates, You have the following data on Per Capita Income in 1987 and the % Births that are "Low Birth Weight" across a sample of states: STATE Per Capita Income of Births of "Low Birth (as of 1987) Weight" (as of 1988) Alaska $13,263 5.0 Colorado $12,271 7.8 Delaware $12,785 7.4 Georgia $11,406 8.4 lowa $11, 198 5.4 Louisiana $8,961 8.8 Maine $10,478 4.8 Minnesota $12,281 5.0 Nebraska $11, 139 5.5 New York $13, 167 7.8 Ohio $11,323 6.9 Oregon $11,045 5.2 South Dakota $8,910 4.7 Utah $9,288 5.7 Wisconsin $11,417 5.4 Source: Statistical Abstracts of the United States, 1991General Procedure for Transforming Data You must always start by looking at a scatterplot of your original data, and examining the pattern. Are there outliers or influential points? What is the shape of the curve? The shape is a guide to choosing a likely transformation. If the points seem to lie in a straight line, you may not need to transform the data at all; you may have a linear relationship. If the explanatory variable involves time, particularly in years, you may want to change the variable to a form easier to work with. For example, if you were studying the U.S. population during the 1800's, looking for the effect of the Civil War, you might pick 1800 to be "zero." Then figure your explanatory variable in terms of years elapsed since 1800: 1820 becomes 20. Remember to "Back-Transform" When you Predict y-Values Remember that, whether you work with your calculator or a spreadsheet, you'll have results expressed simply in x and y. The correct variable for prediction is y . And either variable may actually be transformed (In, exponential, square, square root, and so on). Things to Avoid If your transformation involves taking a logarithm, remember that logarithms are undefined for zero and negative numbers. Questions 1 through 6 work with the length of the sidereal year vs. distance from the sun. The table of data is shown below. Planet Distance from Sun Years (as a In(Dist) In(Year) (in millions of fraction of Earth miles) years Mercury 36.19 0.2410 3.5889 -1.4229 Venus 67.63 0.6156 4.2140 0.4851 Earth 93.50 1.0007 4.5380 0.0007 Mars 142.46 1.8821 4.9591 0.6324 Jupiter 486.46 11.8704 6.1871 2.4741 Saturn 893.38 29.4580 6.7950 3.3830 Uranus 1,794.37 84.0100 7.4924 4.4309 Neptune 2,815.19 164.7800 7.9428 5.1046 Pluto 3,695.95 248.5400 8.2150 5.5156 Enter the original data in L1 and L2 (that is, the Distance from the Sun and Years). You may manually type in L3 and L4 but it's faster to use your calculator's STAT -> edit... Make L3 = In(L1) and L4 = In(L2). Verify that this matches the columns given above. Don't worry about the small discrepancies you may find due to rounding and the number of decimal places shown on your calculator. If your results differ from the values above, double-check your original entries
