EBK STATISTICS FOR THE BEHAVIORAL SCIEN
3rd Edition
ISBN: 9781506386249
Author: PRIVITERA
Publisher: VST
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Chapter 16, Problem 4FP
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Determine why in the method of least squares it is necessary to square the deviation of each data point from the regression line.
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A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is
weight = -5.25 +0.1696 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what
was his residual? What does that say about him?
A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.69 + 0.1656 length. A newborn was 48cm long and weighed 33kg. According to the regression model, what was his residual? What does that say about him?
A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight=−5.82+0.1601 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?
Chapter 16 Solutions
EBK STATISTICS FOR THE BEHAVIORAL SCIEN
Ch. 16.2 - Prob. 1.1LCCh. 16.2 - Prob. 1.2LCCh. 16.2 - Prob. 1.3LCCh. 16.4 - Prob. 2.1LCCh. 16.4 - Prob. 2.2LCCh. 16.4 - Prob. 2.3LCCh. 16.5 - Prob. 3.1LCCh. 16.5 - Prob. 3.2LCCh. 16.6 - Prob. 4.1LCCh. 16.6 - Prob. 4.2LC
Ch. 16.6 - Prob. 4.3LCCh. 16.8 - Prob. 5.1LCCh. 16.8 - Prob. 5.2LCCh. 16.8 - Prob. 5.3LCCh. 16.9 - Prob. 6.1LCCh. 16.9 - Prob. 6.2LCCh. 16.9 - Prob. 6.3LCCh. 16.13 - Prob. 7.1LCCh. 16.13 - Prob. 7.2LCCh. 16.13 - Prob. 7.3LCCh. 16 - Prob. 1FPCh. 16 - Prob. 2FPCh. 16 - Prob. 3FPCh. 16 - Prob. 4FPCh. 16 - Prob. 5FPCh. 16 - Prob. 6FPCh. 16 - Prob. 7FPCh. 16 - Prob. 8FPCh. 16 - Prob. 9FPCh. 16 - Prob. 10FPCh. 16 - Prob. 11FPCh. 16 - Prob. 12FPCh. 16 - Prob. 13CAPCh. 16 - Prob. 14CAPCh. 16 - Prob. 15CAPCh. 16 - Prob. 16CAPCh. 16 - Prob. 17CAPCh. 16 - Prob. 18CAPCh. 16 - Prob. 19CAPCh. 16 - Prob. 20CAPCh. 16 - Prob. 21CAPCh. 16 - Prob. 22CAPCh. 16 - Prob. 23CAPCh. 16 - Prob. 24CAPCh. 16 - Prob. 25CAPCh. 16 - Prob. 26CAPCh. 16 - Prob. 27CAPCh. 16 - Prob. 28CAPCh. 16 - Prob. 29CAPCh. 16 - Prob. 30PRCh. 16 - Prob. 31PRCh. 16 - Prob. 32PRCh. 16 - Prob. 33PRCh. 16 - Prob. 34PR
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardThe weight (in pounds) and height (in inches) for a child were measured every few months over a two- The equation ý = 17.4 + 0.5x is called the least- squares regression line because it year period. The results are displayed in the scatterplot. O is least able to make accurate predictions for the data. O makes the strongest association between weight and height. A Child's Weight and Height 40 O minimizes the sum of the squared distances from the actual y-value to the predicted y-value. 36 O maximizes the sum of the squared distances from the actual y-value to the predicted y-value. 32 28 24 20 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 4042 Weight (Pounds) Height (Inches)arrow_forward
- Please help mearrow_forwardThe average gestational age (time from conception to birth) of a newborn infant is about 40 weeks. The following data presents the gestational age in weeks and corresponding mean birth weight in pounds for female infants born in Canada. Find the least-squares regression line for predicting the birth weight from the gestational age. You should be able to grab the data in the table, copy it, and paste it in Excel. You would then select the data in Excel, Insert a Scatter Chart and then under Trendline, check the two boxes at the bottom to display the equation and the R-squared. Gestational Age Birth Weight 36 6.1 37 6.6 38 7.0 39 7.4 40 7.7 41 7.9 42 8.0 43 8.1 A. y= 3.2787x + 15.402 B. y= 15.402x + 3.2787 C. y= 0.2857x - 3.9357 D. Y= 3.9357X + 0.2857arrow_forwardThe relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y-hat = -0.0127 + 0.0180x. Wendall drinks 4 beers and has a blood alcohol level of .08. What is Wendall’s residual?arrow_forward
- The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it is least able to make accurate predictions for the data. makes the strongest association between weight and height. minimizes the sum of the squared distances from the actual y-value to the predicted y-value. maximizes the sum of the squared distances from the actual y-value to the predicted y-value.arrow_forwardA recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. d. What percentage of variability in resting heart rate can be explained by variability inhours exercised?arrow_forwardCompute the least-squares regression line for predicting the price of milk from the price of eggs. Round the slope and -intercept to at least four decimal places.arrow_forward
- Compute the least-squares regression line for predicting the price of milk from the price of eggs. Round the slope and y-intercept to at least four decimal places.arrow_forwardAn engineer wants to determine how the weight of a gas-powered car, x, affects the gas mileage, y. Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a hybrid gas and electric car? Why and why not?arrow_forwardWhich pair of h0/h1 is used in the two sided test for the slope of a simple linear regression?arrow_forward
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