
Concept explainers
Answer true or false to each of the following statements and explain your answers.
a.
b. When there are errors in the measurements of the predictor variables, statistical inferences in
c. A nonrepresentative sample of the population of interest will have no effect on the regression model that is obtained.

a).
Correlation among values of the response variable underestimates the common conditional standard deviation. This produces larger values of t-statistics for testing utilities of predictors or F-statistics for utility of the regression, leading to rejection of the null hypothesis when it is true or more often.
Thus, the statement is False.
b).
The presence of measurement errors increases the variation in the data unnecessarily. The inferences drawn by analyzing a data with excessive error are unreliable.
Therefore, the statement is True.
Step by stepSolved in 3 steps

- . A random sample consisting of 200 business executives working in the Downtown area is drawn and they were asked to answer a set of questions. One question in the survey asked about their annual salary and another about their annual expenses on luxury goods. We regress the spending on salary, and the regression has R2 = 0.884. Interpret the result of the R2 value in this context. “Despite the high value of R2, a linear regression model may not be appropriate.” Comment.arrow_forwardAnswer true or false to each of the following statements and explain your answers. a. Prior knowledge about the relationship between the response variable and predictor variables should not be used in the model building process. b. It is never appropriate to use data from an observational study to perform a regression analysis. c. In multiple linear regression, there is no guarantee that the model building process will find the “true” model relating the response variable to the predictor variables.arrow_forward10. Answer the following... What is linear regression used for? How do researchers set up and use the linear regression procedure to predict unknown Y scores? What is the symbol for a predicted Y score and what is it called?arrow_forward
- Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) X1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model. was fit to the data. Part of the printout follows: Parameter Estimates T FOR 0 ERROR PARAMETER = 0 PROB>ITI PARAMETER STANDARD VARIABLE DF ESTIMATE INTERCEPT 1 -373.526392 1258.1243396 -0.297 0.7676 SPEED 1 104.838940 22.36298195 4 688 0.0001 сHP 1 3.571850 3.89422935 0.917 0.3629 Identify and interpret the estimate of B2-arrow_forwardcan someone produce SPSS results by including the the intercept (a.k.a. the constant), standard error of estimate, unstandardized regression coefficient, the p-value for the unstandardized coefficient, R-square, Beta (i.e. standardized regression coefficient) using Excel with this given data? Overall: 3.4, 2.9, 2.6, 3.8, 3.0, 2.5, 3.9, 4.3, 3.8, 3.4, 2.8, 2.9, 4.1, 2.7, 3.9, 4.1, 4.2, 3.1, 4.1, 3.6, 4.3, 4.0, 2.1, 3.8, 2.7, 4.4, 3.1, 3.6, 3.9, 2.9, 3.7, 2.8, 3.3, 3.7, 4.2, 2.9, 3.9, 3.5, 3.8, 4.0, 3.1, 4.2, 2.9, 3.9, 3.5, 3.8, 4.0, 3.1, 4.2, 3.0, 4.8, 3.0, 4.4, 4.4, 3.4, 4.0, 3.5 Teach: 3.8, 2.8, 2.2, 3.5, 3.2, 2.7, 4.1, 4.2, 3.7, 3.7, 3.3, 3.3, 4.1, 3.1, 2.9, 4.5, 4.3, 3.7, 4.2, 4.0, 3.7, 4.0 2.9, 4.0, 3.3, 4.4, 3.4, 3.8, 3.7, 3.1, 3.8, 3.2, 3.5, 3.8, 4.4, 3.7, 4.00, 3.4, 3.2, 3.8, 3.7, 4.3, 3.4, 4.0 3.1, 4.5, 4.8, 3.4, 4.2, 3.4 Exam: 3.8 3.2, 1.9, 3.5, 2.8, 3.8, 3.8, 4.1, 3.6, 3.6, 3.5, 3.3, 3.6, 3.8, 3.8, 4.2, 4.1, 4.0, 4.3, 4.2, 4.0, 4.1, 2.7, 4.4, 4.4, 4.3, 3.6, 4.1, 4.2, 3.6,…arrow_forward12. A consumer advocacy group recorded several variables on 140 models of cars. The resulting information was used to produce the following regression output that relates the city gas mileage (in mpg) and the engine displacement (in cubic inches). The regression equation is mpg:city= 33.4 0.0624 displacement Predictor Constant SE Coef T P 0.7762 43.00 0.000 displacement -0.0624 0.003810 0.000 S 3.13923 = R-Sq 66.0% R-Sq (adj) = 65.8% a. We have a car that has an engine with 150 cubic inches. Based on this output, what city gas mileage would you predict for this car? Coef 33.4 b. Based on this output what is the correlation between city gas mileage and displacement? C. I value: The test statistics for testing the slope is zero is missing. Calculate this The group o also recorded the power of the engine (in horsepower) for each car. The following regression output was produced. Predictor Constant horsepower The regression equation is mpg:city = 32.2 0.0572 horsepower Coef SE Coef 32.2 T…arrow_forward
- 24) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.arrow_forwardIs IQ related to GPA?If a student’s IQ is 117, what GPA would you predict?How much of the variation in GPA is explained by IQ?What can you conclude based upon the standard error of the estimate?arrow_forwardState the null hypothesis for this study. . You can reject Ho based on sig. value but the value of r is a weak How can you explain that? How do you conclude this result? Based on this position, write the likely regression equation. Write down statistics representation of the correlation in APA format .... Please answer number 5. tqarrow_forward
- Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 1150 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 25 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 1133 Gy, with a sample standard deviation of 02 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is appraximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level af significance, to support that H, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 1150 Cy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for…arrow_forwardThe table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, y = bo + b₁x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Studying 2 3 Midterm Grades 71 72 Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places. Answer How to enter your answer (opens in new window) 4 5 6 73 77 86 Tables Table Copy Data Keypad Keyboard Shortcutsarrow_forwardIf the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. Select one: True Falsearrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





