Example 15.11) The following table shows the marks obtained in two tests by 10 students:Marks in Ist Test (X)9.8.876.1047Marks in 2nd Test (Y)87108109.86.(a) Find the least square regression line of Y on X. /(b) Test the hypothesis that marks in the two tests are linearly related.

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Answered: Example 15.11) The following table…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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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?
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆy=a+bxa=0.313b=0.145 (a) Write the equation of the Least Squares Regression line of the formˆy= + x(b) Which is a possible value for the correlation coefficient, r? -0.666 -1.772 1.772 0.666 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 4 years in a certain country, how much will the happiness index change? Round to two decimal places.Use the regression line to predict the happiness index of a country with a life expectancy of 65 years. Round to two decimal places.
The new manager of an Information Technology company collected data for a sample of 20 computer programmers in the organization to perform a multiple regression analysis on the structure of their salaries. The aim of this manager in this exercise is to determine if the Salary (y) of a hired computer programmer was related to the years of Experience (??) in the organization and also the Score (??) of the programmers during their first interview aptitude test scores. The years of experience, score on the aptitude test and the corresponding annual salary (in thousands of Ghana cedis) for a sample of the 20 programmers is shown in the Regression statistics table below; Experience (??) (in years) Score (??) (out of 100%) Salary (y) (GH¢ 000) 4 78 24 7 100 43 1 86 23.7 5 82 34.3 8 86 35.8 10 84 38 0 75 22.2 1 80 23.1 6 83 30 6 91 33 9 88 38 2 73 26.6 10 75 36.2 5 81 31.6…
The new manager of an Information Technology company collected data for a sample of 20 computer programmers in the organization to perform a multiple regression analysis on the structure of their salaries. The aim of this manager in this exercise is to determine if the Salary (y) of a hired computer programmer was related to the years of Experience (??) in the organization and also the Score (??) of the programmers during their first interview aptitude test scores. The years of experience, score on the aptitude test and the corresponding annual salary (in thousands of Ghana cedis) for a sample of the 20 programmers is shown in the Regression statistics table below; Experience (??) (in years) Score (??) (out of 100%) Salary (y) (GH¢ 000) 4 78 24 7 100 43 1 86 23.7 5 82 34.3 8 86 35.8 10 84 38 0 75 22.2 1 80 23.1 6 83 30 6 91 33 9 88 38 2 73 26.6 10 75 36.2 5 81 31.6…
Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(
Data on 12 randomly selected athletes was obtained concerning their cardiovascular fitness (measured by time to exhaustion running on a treadmill) and performance in a 20-km ski race. Both variables were measured in minutes and a regression analysis was performed. Ski = 87 1.6-Treadmill Coefficients Estimate Std. Error 0.5 (Intercept) Treadmill 1.03 87 -1.6 Is there sufficient evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance? (a). The test statistic is (use four decimal places) (b). The p-value is (use four decimal places) (c). At the 5% significance level, we [Select an answer the null hypothesis and conclude that there is Select an answer evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance.
Data on 220 reported crimes is collected from district X in 2016. Suppose CS denotes the total cost to the state of offering crime protection services to this district (in thousand dollars), LEOP denotes the number of law enforcement officers on patrol, DTP denotes the damage to public and private property (in thousand dollars), CCTV denotes the number of CCTV cameras installed in the district, and Prison denotes the number of prison inmates The following table shows the results of a few regressions of the total cost to the state. Dependent variable: total cost to the state (in thousand dollars) Regressor (1) (2) (3) (4) 12.32 17.99 14.55 18.1 LEOP (0.52) (0.84) (2.25) (0.82) 0.73 0.59 0.75 DTP (0 12) (0.04) 0.73 (0.06) CCTV (0.13) 2.11 2.12 (0.39) 288.5 (4 14) Prison (0.5) 182.5 191.6 219.95 Intercept (11.52) (6.68) (5.26) 0.64 0.75 0.12 0.75 R 220 220 220 220 Heteroskedasticity-robust standard errors are given in parentheses under coefficients. Which of the following statements…
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Q.8). In a regression calculation, a researcher finds that the explanatory variable x has mean 100 and SD 10, and the response variable y has mean 250 and SD 40. The regression equation is found to be y^ = 450 and y? 2x. What is the correlation between x (a) cannot tell from the information available (b) -0.8 (c) -0.5 (d) 0.4 (e) 0.1 Q.10) a) What are the differences between the data and information? b) Explain the differences between the types of Statistics
A survey on lamb farms was conducted and data were collected on the followingvariables from a random sample of 30 farmers.Y = average live weight of ewes (kg)X1 = area of grazing land (m2) X2 = proportion of farm area that cannot be cultivatedX3 = proportion of area closed for lambs before weaning True or False1. About the computed correlation coefficients?a. weak positive linear relationship between average live weight of ewes and proportion offarm area that cannot be cultivated. b.very weak negative linear relationship between average live weight of ewes and area ofgrazing land. c. Both are Trued. Both are False
Suppose the following regression equation was generated from the sample data of 50 cities relating number of cigarette packs sold per 1000 residents in one week to tax in dollars on one pack of cigarettes and if smoking is allowed in bars: PACKS, 58803.462982-1005.438507TAX, +284.030008BARS, + BARS, 1 if city / allows smoking in bars and BARS,= 0 if city i does not allow smoking in bars. This equation has an R² value of 0.305162, and the coefficient of BARS, has a value of 0,088136. Which of the following conclusions is valid? Answer Keypad Keyboard Shortcuts m Tables O If there is no cigarette tax in a city that allows smoking in bars, the approximate number of cigarette packs sold per 1000 people is 58803. O According to the regression equation, cities that allow smoking in bars have lower cigarette sales than cities that do not allow smoking in bars. O More than half of the variation in cigarette sales is explained by cigarette taxes and whether or not a city allows smoking in bars.…
The following results are from data concerning the amount withdrawn from an ATM machine based on the amount of time spent at the ATM machine (SECONDS) and the gender, FEMALE (dummy variable = 1 for females and = 0 for males) and an interaction term, SECONDS*FEMALE Based on the regression results, if a male and female each spend the same amount of time at the ATM machine (say 27 seconds), how much more (or less) will a male withdraw? (if a male withdraws more then your answer should be a positive number and if a male withdraws less then your answer should be a negative number? (please express your answer using 1 decimal places)

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Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 9. 8 8 7 6. 10 4 9. 7 Marks in 2nd Test (Y) 7 7 10 8 10 6. 6. (a) Find the least square regression line of Y on X. (b) Test the hypothesis that marks in the two tests are linearly related.