Concept explainers
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 10-5 on page 493. Use a 0.05 significance level.
7. Height and Weight Heights (cm) and weights (kg) are measured for 100 randomly selected adult males (from Data Set 1 “Body Data” in Appendix B). The 100 paired measurements yield
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Essentials of Statistics (6th Edition)
- In the regression model ŷ = a + bx, a and b are the: omitted variables O sample statistics O random variables O population parametersarrow_forwarda) Calculate the sample correlation coefficient r (show all your work).b) Calculate the regression line (you may use technology, but you should write up the details).c) Use the regression line obtain in b. to predict the value of y for x = 0.3 year.d) Use the regression line obtain in b. to predict the value of y for x = 0.8 year.arrow_forwarda. Estimate the regression line and also write the prediction equation. y = 83.4578-5.8795 x y = 5.8795 + 83.4578 x ŷ ŷ= = -5.8795 + 83.4578 x = 83.4578 + 5.8795 xarrow_forward
- Determine the statistical test that should be conducted before conducting linear regression? a. Normality test b. Variance Homogeneity test c. Correlation d. Data transformationarrow_forwardA study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Lovers 8 3 1 3 6 3 4 8 GPA 2.1 2.7 3.2 2.6 2.8 3.1 2.9 2.2 Use the model to predict the GPA of a college student who as had 3 lovers.GPA = (Please round your answer to one decimal place.) Interpret the slope of the regression line in the context of the question: For every additional lover students have, their GPA tends to decrease by 0.13. The slope has no practical meaning since a GPA cannot be negative. As x goes up, y goes down. Interpret the y-intercept in the context of the question: The best prediction for the GPA of a student who has never had a lover is 3.29. The y-intercept has no practical meaning for this study. If a student has never had a lover, then that student's GPA will be 3.29. The average GPA for all students is predicted to be 3.29.arrow_forwarda. Draw a scatter diagram for the data. b. Draw a regression line of y on x. c. Determine the equation of the line of best fit.arrow_forward
- The table below shows the average monthly rainfall in inches for Los Angeles, California. Which model best represents the data set? Month 1 2 3 4 7 8 10 11 12 Rainfall 3.33 3.68 3.140.83 0.31 0.06 0.01 0.13 0.32 0.37 1.05 1.91 O y = 0.09x² – 1.43x + 5.51 Oy = -1.43x + 5.51 O y = 0.01x? +1.43x + 5.51 O y = 1.43x +5.51arrow_forwardInterpreting a Computer Display. In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the StatCrunch display and answer the given questions or identify the indicated items. The display is based on Data Set 5 “Family Heights” in Appendix B. Height of Son Identify the following: a. The P-value corresponding to the overall significance of the multiple regression equation b. The value of the multiple coefficient of determination R2 c. The adjusted value of R2arrow_forwardCalculate the best (most complex/sophisticated/stable) measure of central tendency allowed for the following data. The variable is favorite month (Where January = 1, February = 2, etc.) Explain. 3, 9, 9, 4, 2, 7, 1arrow_forward
- An educational psychologist studies the effect of frequent testing on retention of course material. In one of the professors sections, students are given quizzes each week. The second section receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Frequent Quizzes Two Exams n=15 n=15 M=82 M=78 S2= 7.07 S2=13.57 a. Does the data indicate that testing frequency significantly increases performance at the .01 level of signifigance. b. what percent of increase in performance was due to the increase in testing frequency?arrow_forwardExplain whether each scenario below is a regression, classification, or unsupervised learn- ing problem. If it is a supervised learning scenario, indicate whether we are more interested in inference or prediction. Finally, provide in each case the number of observations, n, and the number of predictors, p. (1) An online retailer must decide whether to display advertisement A or advertisement B to each customer on the basis of collected customer demographics (age, income, zip code, and gender). A set of 150 of its customers have already expressed a preference for one advertisement or the other. (2) A policy analyst is interested in discovering factors that are associated with the crime rate across different U.S. cities. For each of 500 cities, the policy analyst gathers the following data: the crime rate, unemployment rate, population, median income, median home price, and state. (3) The the channel owner to see where the subscribers are located, their age and gender, the times and days…arrow_forwardWhat is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time Score 3 4 73 16 2 15 10 3 95 61 67 67 88 90 75 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Hg: ?v = 0 H: ?v + 0 Round to 2 decimal places. The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. O There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that there is a correlation between the…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL