Statistics for the Behavioral Sciences
3rd Edition
ISBN: 9781506386256
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 16, Problem 30PR
To determine
Identify the predictor variable and the criterion variable in the study.
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If there is no significant correlation between the response and explanatory variables, would the slope of the regression line be (a) positive (b) negative (c) zero?
A researcher was investigating variables that might be associated with the academic performance of high school students. The data included the average Math SAS score of all high school seniors in the city that took the exam (labeled as the variable SAT-M), the average number of dollars per pupil spent on education by the city (labeled as the variable $Per Pupil), and the percentage of high school seniors in the city that took the exam (labeled as the variable %Taking). The researcher ran the following multiple linear regression model as SAT-M=Beta0 + Beta1($Per Pupil) + Beta2(%Taking). This model was fit to the data using the method of least-squares, results shown inside of table within photo.
If we want to test using ANOVA F-test with hypotheses Ho: Beta1=Beta2=0 versus H1: at least one of the Beta is not 0, what would the value of our F-statistic mean?
Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below.
Say how you know from the output that there actually is a significant linear relationship between a male customer’s age at death and his father’s age at death.
State the value of the coefficient of Father’s Age (Death) and interpret this value in the context of the problem at hand.State the value of the coefficient of determination in the model and interpret this value in the context of the situation.
Chapter 16 Solutions
Statistics for the Behavioral Sciences
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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- Olympic 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_forwardLife insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below Examine both the scatterplot and the correlation matrix provided above. Comment on the apparent relationship between the customer’s age at death and their father’s age at death in the plot. Explain how the information in the correlation matrix supports your conclusionarrow_forwardIn a simple linear regression model with one predictor variable, what is the coefficient of determination (R-squared) if the Pearson's correlation coefficient between the predictor and response variable is 0.6?arrow_forward
- If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?arrow_forwardThe monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…arrow_forwardA mail-order business selling personal computer supplies, software and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect the warehouse distribution costs. Data collected over 24 random months contain the warehouse’s distribution cost (in thousands of Rands), the sales (in thousands of Rands) and the number of orders received. A multiple linear regression model was fitted to the data by using Stat1.2. Use the output to answer the questions that follow by typing only the letter of the correct option in the answer boxes. Variablesy: Warehouse Distribution Costx1: Salesx2: Number of Orders Model Fitting StatisticsR2 = 0.8504Adj R2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates…arrow_forward
- The systolic blood pressure dataset (in the third sheet of the spreadsheet linked above) contains the systolic blood pressure and age of 30 randomly selected patients in a medical facility. What is the equation for the least square regression line where the independent or predictor variable is age and the dependent or response variable is systolic blood pressure? Y=__________ X + ______________ Patient 7 is 67 years old and has a systolic blood pressure of 170 mm Hg. What is the residual? __________ mm Hg Is the actual value above, below, or on the line? What is the interpretation of the residual? (difference in actual &predicated bp, difference in age, the amount of systolic changes)arrow_forwardA fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of regressions coefficients and write down the simple linear regression model.arrow_forwardon the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?arrow_forward
- The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of varieties of Kellogg's cereal. Find the predictive regression equation of the number of calories on the amount of sugar. Sugar (grams) 6 15 12 11 8 6 7 4 9 14 20 13 3 Calories 120 200 150 110 120 80 190 120 120 190 190 120 120arrow_forwardThe Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?arrow_forwardIn an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 17 wines, a model was created using the percentages of alcohol to predict wine quality. From the results of that regression, b1=0.4386 and Sb1=0.1141. a. At the 0.05 level of significance, is there evidence of a linear relationship between the percentage of alcohol and wine quality? b. Construct a 95% confidence interval estimate of the population slope, β1. b. The 95% confidence interval is __ ≤ β1 ≤ __ (Round to three decimal places as needed.)arrow_forward
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