Regression and Predictions. Exercises use

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 102. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5. Gas Prices One gas station not included in the table below had a listed price of $2.78 for regular gas. Find the best predicted price of premium gas at this station. Is the result close to the actual price of $2.93 for premium gas?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-2.In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5. Sports Find the best predicted circumference of a marble with a diameter of 1.50 cm. How does the result compare to the actual circumference of 4.7 cm? Baseball Basketball Golf Soccer Tennis Ping-Pong Volleyball Softball Diameter Circumference Volume

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-2.In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5. Gas Prices Using the data from the preceding exercise, find the best predicted price for midgrade gas for a station that posted $2.78 as the price of regular gas. Is the result close to the actual price of $2.84 for midgrade gas?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-2.In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5. Sports Using the data from the preceding exercise, find the best predicted volume of a marble with a diameter of \(1.50 \mathrm{~cm}\). How does the result compare to the actual volume of \(1.8 \mathrm{~cm}^{3}\)? Equation Transcription: Text Transcription: 1.50 cm 1.8 cm^3

Large Data Sets. Exercises 29–32 use the same Appendix B data sets as Exercises 29–32 in Section 10-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted values following the prediction procedure summarized in Figure 10-5. IQ and Brain Volume Refer to Data Set 6 in Appendix B and use the paired data consisting of IQ score and brain volume \((\mathrm{cm} 3)\) . Find the best predicted IQ score for someone with a brain volume of \(1000 \mathrm{~cm} 3\). Equation Transcription: Text Transcription: (cm 3) 1000 cm 3

Problem 32 BB Equivalent Hypothesis Tests Explain why a test of the null hypothesis H0:? = 0 is equivalent to a test of the null hypothesis H0:?1 = 0, where ? is the linear correlation coefficient for a population of paired data, and ?1 is the slope of the regression line for that same population.

Large Data Sets. Exercises 29–32 use the same Appendix B data sets as Exercises 29–32 in Section 10-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted values following the prediction procedure summarized in Figure 10-5. Flight Delays Refer to Data Set 15 in Appendix B and use the departure delay times and the arrival delay times. Find the best predicted arrival delay time for a flight with no departure delay.

Large Data Sets. Exercises 29–32 use the same Appendix B data sets as Exercises 29–32 in Section 10-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted values following the prediction procedure summarized in Figure 10-5. Earthquakes Refer to Data Set 16 in Appendix B and use the magnitudes and depths from the earthquakes. Find the best predicted depth of an earthquake with a magnitude of 1.50.

Least-Squares Property According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. Refer to the data in Table a. Find the sum of squares of the residuals. b. Show that the regression equation \(y^{\wedge}=120+2.00 x) results in a larger sum of squares of residuals. Equation Transcription: Text Transcription: y^{\wedge}=120+2.00 x

Large Data Sets. Exercises 29–32 use the same Appendix B data sets as Exercises 29–32 in Section 10-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted values following the prediction procedure summarized in Figure 10-5. Word Counts of Men and Women Refer to Data Set 17 in Appendix B and use the word counts measured from men and women in couple relationships listed in the first two columns of Data Set 17. Find the best predicted word count for a woman who is in a couple relationship with a man having a word count of 10,000.

Effects of an Outlier Refer to the Minitab­-generated scatterplot given in Exercise 11 of Section 10­-2. a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point with coordinates (10, 10), use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b).

Effects of Clusters Refer to the Minitab-­generated scatterplot given in Exercise 12 of Section 10-­2. a. Using the pairs of values for all 8 points, find the equation of the regression line. b. Using only the pairs of values for the 4 points in the lower left corner, find the equation of the regression line. c. Using only the pairs of values for the 4 points in the upper right corner, find the equation of the regression line. d. Compare the results from parts (a), (b), and (c).

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­5. Lemons and Car Crashes Find the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports.

Notation and Terminology If we use the paired height/pulse data for females from Data Set 1 in Appendix B, we get this regression equation: y ^ = 73.9 + 0.0223 x , where x represents height (cm) and the pulse rate is in beats per minute. What does the symbol y ^ represent? In this case, what does the predictor variable represent? What does the response variable represent?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­-5. PSAT and SAT Scores One subject not included in the given table had a PSAT score of 229. Find the best predicted SAT score for this student. Is the result close to the reported value of 2400? Given that the data are from volunteered responses, are the results valid?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­-5. Campus Crime Find the best predicted number of burglaries for Ohio State, which had an enrollment of 51,800 students. Is the predicted value close to 329, which was the actual number of burglaries?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­-5. Altitude and Temperature At 6327 ft (or 6.327 thousand feet), the author recorded the temperature. Find the best predicted temperature at that altitude. How does the result compare to the actual recorded value of \(48^\circ \mathrm F\)? ________________ Equation Transcription: Text Transcription: 48^oF

Problem 2 BSC Best-Fit Line In what sense is the regression line the straight line that “best” fits the points in a scatterplot?

Problem 3 BSC Correlation and Slope Formula 10-3 shows that the slope of a regression line can be found by evaluating r • sy/sx. What do we know about the graph of the regression line if r is a positive value? What do we know about the graph of the regression line if r is a negative value?

Notation What is the difference between the regression equation y ^ = b 0 + b 1 x and the regression equation \(\mathrm {y = \beta\ 0 + \beta\ 1\ x}\)? ________________ Equation Transcription: y ^ = b 0 + b 1 x Text Transcription: y ^ = b 0 + b 1 x y = beta 0 + beta 1 x

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­-5. Town Courts The court for the town of Beekman had income of $83,941 (or $83.941 thousand). Find the best predicted salary for the justice. Is the result close to the actual salary of $26,088?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­-5. Auction Bids An item not included in the table is a pair of New York Knicks tickets. The auctioneer started the bidding at $300. Find the best predicted winning bid. Is the result close to the actual winning bid of $250?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­-5. Galaxy Distances The cluster Hydra has a measured redshift of 0.0126. Find the best predicted distance to that cluster. Is the result close to the actual distance of 0.18 billion light-­years?

Making Predictions. In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10­5. Old Faithful For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the time intervals (min) after the eruptions. The linear correlation coefficient is r = 0.687 and the regression equation is y ^ = 47.4 + 0.180 x , where x represents duration time. The mean of the 40 duration times is 245.0 sec and the mean of the 40 interval times is 91.4 min. What is the best predicted interval time following an eruption with a duration time of 120 min?

Making Predictions. In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10­5. Old Faithful For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the heights (ft) of the eruptions. The linear correlation coefficient is r = 0.0915 and the regression equation is y ^ = 119 + 0.0331 x , where x represents duration time. The mean of the 40 duration times is 245.0 sec and the mean of the 40 heights is 127.2 ft. What is the best predicted height of an eruption with a duration time of 120 min?

Making Predictions. In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10­5. Heights of Fathers and Sons The heights (in inches) of a sample of 10 father/son pairs of subjects were measured. The linear correlation coefficient is r = 0.149 and the regression equation is y ^ = 66.8 + 0.016 x , where x represents the father's height. The mean of the 10 father heights is 69.7 in. and the mean of the 10 son heights is 68.0 in. What is the best predicted height of a son who has a father with a height of 72.0 in.?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­5. Diamond Prices Not included in the table below is a diamond with a weight of 1.50 carats. Find the best predicted price for this diamond. Is the result close to the actual price of $16,097? What is wrong with predicting the price of a 1.50­carat diamond?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­5. Measuring Seals from Photos Find the best predicted weight of a seal if the overhead width measured from a photograph is 2 cm. Can the prediction be correct? What is wrong with predicting the weight in this case?

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­5. Car Repair Costs Find the best predicted repair costs for a full­rear crash for a Volkswagon Passat, given that its repair cost from a full­front crash is $4594. How does the result compare to the $982 actual repair cost from a full­rear crash?

Making Predictions. In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10­5. Cereal Killers The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) were recorded for a sample of 16 different cereals. The linear correlation coefficient is r = 0.765 and the regression equation is y ^ = 3.46 + 1.01 x , where x represents the amount of sugar. The mean of the 16 amounts of sugar is 0.295 grams and the mean of the 16 calorie counts is 3.76. What is the best predicted calorie count for a cereal with a measured sugar amount of 0.40 g?

Problem 9 BSC Finding the Equation of the Regression Line. In Exercises, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x 10 8 13 9 11 14 6 4 12 7 5 y 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74

Problem 10 BSC Finding the Equation of the Regression Line. In Exercises, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x 10 8 13 9 11 14 6 4 12 7 5 y 7.46 6.77 12.74 7.11 7.81 8.84 6.08 5.39 8.15 6.42 5.73

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­5. Blood Pressure Measurements Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 100 mm Hg.

Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10­2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10­5. Crickets and Temperature Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute. What is wrong with this predicted value?