Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group ofY values that is normally distributed. (2) The means of these normal distributions of Y values all lie on the regression line. (3) The standard deviations of these normal distributions are equal. Multiple Choice

Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group ofY values that is normally distributed. (2) The means of these normal distributions of Y values all lie on the regression line. (3) The standard deviations of these normal distributions are equal. Multiple Choice

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 16CR: XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ...

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XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?
Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.
Which of the following is not one of the statistical assumptions behind linear regression? a. The residuals should not be autocorrelated. b. The variance of Y for all combinations of X variable values should be constant. c. The X variables should be normally distributed. d. The residuals should be normally distributed.
Which of the following is/are true if the coefficient of determination between the response and the predictor variables is 81 percent based on a random sample of size n i. the pearson's sample correlation coefficient is +0.9 ii. this means that 19 percent of the total variation in the response variable remains unexplained by tge simple linear regression model that uses the given predictor variable iii both i and ii iv neither i and ii
Which of the following is not an assumption of a linear regression? A The residuals follow a normal distribution. B The variance from the regression line is the same C The slope of the relationship between the X and Y variables is constant. D The line minimizes the sum of the squared vertical difference between the observation and the line.
Which of the following is not a formal condition for inference about a regression estimate? Sampling independence of bivariate observations Linearity between variables X and Y Normality in the distribution of residuals Heteroscedasticity between X and Y variables
6. As the value of r approaches ±1, what does it indicate about the following? The consistency that Ys are paired with X The variability of the Y scores at each X The closeness of Y scores to the regression line at each X The accuracy with which we can predict Y if X is known.
True or false: “If the errors in a regression model contain ARCH, they must be serially correlated.”
17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
1. If you accidentally forget to use the robust standard errors option in your regression software, then: A) both your coefficients and standard errors will be different than in case with robust SE B) only your standard errors will be different than in case with robust SE C) only your coefficients will be different than in case with robust SE D) only the R squared will be different than in the case with robust SE 2. We saw that the OLS estimator from a regression of test scores on a dummy for class size (X=1 for STR<20) was positive and equal to 7.4. If average family income is negatively correlated with average class size in California school districts, we can expect the OLS estimator to be: A) larger than the true population value of the difference in means B) smaller than the true population value of the difference in means C) equal to the correlation between test scores and class size D) equal to the true population value of the difference in means
Q. Which of the following is a difference between the White test and the Breusch-Pagan test? a. The White test is used for detecting autocorrelation in a linear regression model, whereas the Breusch-Pagan test is used for detecting heteroscedasticity. b. The White test is used for detecting heteroscedasticity in a linear regression model, whereas the Breusch-Pagan test is used for detecting heteroscedasticity in a quadratic regression model. c. The number of regressors used in the White test is larger than the number of regressors used in the Breusch-Pagan test. d. The number of regressors used in the Breusch-Pagan test is larger than the number of regressors used in the White test.
9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5