In performing a regression analysis involving two numerical variables, we are assuming the variance of X and Y are equal. O the variation around the line of regression is the same for each X value. O that X and Y are independent. O all of the above.
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- 4 Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x 0 2 2 4 4 5 Test score, y Find the regression equation. y=x+ X+ C Test score 80- (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. O A. O B. 0- 0 8 Hours studying 40 43 50 49 62 67 OA. 97.5 OB. 55.2 O C. 60.1 P Test score D. not meaningful 80- 0- 0 8 Hours studying O C. Test score (a) x = 3 hours (c) x = 12 hours 80- (a) Predict the value of y for x = 3. Choose the correct answer below. 0- 0 8 Hours studying O D. OA. 55.2 OB. 52.7 O C. 60.1 O D. not meaningful (b) Predict the value of y…The slope D of the sample regression line provides a measure of O1.the change in the population value of the dependent variable for every unit change In the Independent varlable. O 2. the change in the population average value of the dependent varlable for overy unit change in the independent varlable, 03.the change In the population value of the independent varlable for every unit change in the dependent varlable. 04.the change in the population average value of the independent variable for every unit change in the dependent varlablo. O 5.the change in the estimated population value of the dependent variable for every unit change in the Independent varlable. O 6.the change in the estimated population average value of the dependent variable for every unit change in the independent varlable. O 7. the change in the estimated population value of the independent variable for every unit change in the dependent variable, O 8. the change in the estimated population average value of the…Which of the following is an assumption of the regression model? Select one: a. X and Y are independent variables. b. The errors of prediction are uniformly distributed. c. The error terms of X are dependent on the error terms of Y. d. There exists a linear association between variables X and Y.
- Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.| Find the regression lines of Y on X and X on Y for the following data. EX = 70, EY = 83, EX? = 590, EY² = 755, EXY= 640, n= 10.Recall that R2 is the multiple coefficient of determination and is an indication of the goodness of fit for an estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and SST is the total sum of squares. SSR R2 ST We are given that SST = 1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result to three decimal places.
- repostA researcher would like to predici the dependent variable Y fram the two independent variables X, and Xg for a sample of N = 18 subjecis. Use muliple linear regression to calculate the coefficient of multiple determination and Lest the significance of the overall regression model. Use a significance level a = 0.01. Y 53.2 42.4 56.6 75 32.2 62.9 68.2 26.9 70.1 63 30.9 57,4 52 44.2 70.1 52.9 33 55.9 67.8 35.3 54.9 51.1 49 47.8 39.5 57.4| 46.9 45.7| 52.7 60.5 57.2 43.2 61.1 40.4 42 | 45,7 56.1 42.2 37.3 51.8 | 58.9 53,4 51.9 42.2 47.5 37.1 48 46.8 66 33.8 | 61.7 32.3 53.4 57.5 F= Pvalue - What is your decision for the hypothesis test? O Reject the null hypothesis, H.:B, = B =0 O Fail to reject H, What is your final conclusion? O The evidence supports the claim that one ar more of the regression coefficients is non-zero O The evidence supports the claim that all of the regression coelfficients are zero OThere is insufficient evidence to support the claim that at least one of the regression…21. Which of the following statements is true regarding the sources of variation present in an analysis of regression? SSy is partitioned into variation explained by the regression model and residual variation. If most of the variability in Y is associated with residual variation, then X predicts Y. There are three sources of variation in an analysis of regression: regression variance, residual variance, and error variance. Regression variation measures variability in X, whereas residual variation measures variability in Y.
- Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the valuo of v for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x Stories, y 762 621 508 480 (b) x = 641 feet (d) x = 726 feet 515 491 (a) x= 498 feet (c) x = 810 feet 51 46 44 42 38 37 Find the regression equation. ý=x+ (D (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. OA. OB O B. Oc. OD. 60- 604 60+ 800 B00 G 800 Height (feet) 800 Height (feet) 800 Height (feet) Height (feet) (a) Predict the value of y for x = 498. Choose the correct answer below. OA 40 ОВ. 50 O C. 47 O D. not meaningful (b) Predict the value of y for x 641. Choose the correct answer…Suppose you are given the following x and y values. Assume x is the independent variable and y the dependent variable. x y 13 10 10 11 3 4 29 23 5 8 25 21 8 10 17 15 19 17 31 29 23 24 What is the regression equation? Group of answer choices 2.5296x + 0.7878 0.7878x 2.5296 + 0.7878y 2.5296 + 0.7878xPlease answer A,B, D, F, & G pls and thank you!