Statistics for the Behavioral Sciences, Loose-leaf Version
10th Edition
ISBN: 9781305862807
Author: GRAVETTER
Publisher: CENGAGE L
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Chapter 16, Problem 9P
Does the regression equation from problem 8 account for a significant portion of the variance in the Y scores? Use
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The correlation between two variables x and y is –0.6. If we used a regression line to predict y using x, what percent of the variation in y would be explained?
A professor obtains SAT scores and freshman grade point averages (GPA) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS=22,400, and GPA has a mean of 3.10 with SS=1.26, and SP=84.c. Does the regression equation account for a significant portion of the variance in GPA? Use ?=.05α=.05 to evaluate the F-ratio.
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84.
Find the regression equation for predicting GPA from SAT scores.
What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find r^2.)
Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.
Chapter 16 Solutions
Statistics for the Behavioral Sciences, Loose-leaf Version
Ch. 16 - Sketch a graph showing the line for the equation...Ch. 16 - The regression equation is intended to be the...Ch. 16 - A set of n=18 pairs of scores (X and Y values) has...Ch. 16 - A set of n=15 pairs of scores (X and Y values)...Ch. 16 - Briefly explain what is measured by the standard...Ch. 16 - In general, how is the magnitude of the standard...Ch. 16 - For the following set of data, find the linear...Ch. 16 - For the following data: a. Find the regression...Ch. 16 - Does the regression equation from problem 8...Ch. 16 - For the following scores, X Y 3 8 5 8 2 6 2 3 4 6...
Ch. 16 - Ii. Problem 13 in Chapter 15 examined the...Ch. 16 - A professor obtains SAT scores and freshman grade...Ch. 16 - Problem 14 in Chapter 15 described a study...Ch. 16 - 14. There appears to be some evidence suggesting...Ch. 16 - The regression equation is computed for a set of n...Ch. 16 - 16. a. One set of 10 pairs of scores, X and Y...Ch. 16 - 17. a.A researcher computes the linear regression...Ch. 16 - For the following data: Find the regression...Ch. 16 - A multiple-regression equation with. two predictor...Ch. 16 - A researcher obtained the following multiple...Ch. 16 - 21. Problem 18 in Chapter 15 (p. 526) presented...Ch. 16 - For the data in problem 21, the correlation...Ch. 16 - For the following data, find the...Ch. 16 - A researcher evaluates the significance of a...
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardFor the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracyarrow_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_forward
- For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.arrow_forwardFor the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.arrow_forwardIn a regression context, under what situation is the predicted value for Y equal to the mean of Y?arrow_forward
- A local retail store compared their monthly sales of umbrellas with the amount of rainfall that occured during that month. They computed the following statistics: Rainfall (in) # of umbrellas mean = 4.64 mean = 34.2 SD = 1.17 SD = 13.2 r = 0.8 1. Find the equation for the regression line that predicts the monthly sales of umbrellas from monthly rainfall.arrow_forwardThe adjusted R-squared accounts for the amount of variance explained while also adjusting for the number of independent variables in the linear regression equation. True or Falsearrow_forwardThe higher the difference between the observed value of y and the predicted value of y, the better the regression model is. Select one: O True Falsearrow_forward
- A regression between foot length (response variable in cm) and height (explanatory variable in inches) for 42 students resulted in the following regression equation: y = 10.4 + 0.21x If a student happened to be extraordinarily tall (say, 10ft, just for the fun of it) and had a foot size of 25 cm, how might this affect the slope of the regression line?arrow_forwardPLease help!arrow_forwardFor a group of children, mean age is 10 years with S.D. 2·5 years. The average height of the group is 125 cms with S.D. of 13 cms. The coefficient of correlation between age and height is 0-6. Write the equation of two regression lines and explain their use.arrow_forward
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