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- The degrees of freedom of correlation test is determined by what?What is the Pearson's r correlation coefficient for a sample set of data with values (1,2), (2,3), (3,4), (4,5)?Assume a variable has only 3 observations: x1=1, x2=5, x3=6. What is the variance of this variable x? 8.6 None of others. 4.7 2.9
- What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 9 randomly selected games are shown below. Attendance 24 54 59 17 32 58 30 26 18 Runs 5 14 14 5 7 8 10 6 4 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are:`H0: ` == 0`Ha:` ≠≠ 0 The p-value is: (Round to four decimal places) Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. There is statistically insignificant…Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men. Complete parts (a) through (e) below. 12- 3- :: 3 6 12 b. Examine the pattern of the four points in the upper right corner (from men) only, and subjectively determine whether there appears to be a correlation between x and y for men. Choose the correct answer below. O A. There appears to be a linear correlation because the points form an obvious pattern. B. There does not appear to be a linear correlation because the points do not form a line. O C. There does not appear to be a linear correlation because the points form an obvious pattern. O D. There appears to be a linear correlation because the points form a line. c. Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper right corner (for men) have the same linear correlation…The scatterplot below shows the relationship between two random variables X and Y. (a) Is the correlation a good metric for describing the relationship between X and Y for these data? Why or why not? Regardless of your answer suppose you calculated the sample correlation between X and Y and found that r = -0.15. Explain in one sentence what this means. (b) If, as noted in (a), r = -0.15 then what is the value of the correlation between 2X and 5Y? (c) Based on (b) draw your best approximation to the least squares regression line that fits the data above. Also, make a rough sketch of the corresponding residual plot.
- What is the Pearson's correlation coefficient for a sample of data with values (2, 3), (4, 5), (6, 7), (8, 9), and (10, 11)?7The data obtained in a study on the number of absences in virtual class and the final grades of seven randomly selected students from a mathematics class. The data are shown below. To determine the significance of the correlation coefficient at 0.05 level of significance, what is the calculated or computed value (CV)? Final grade y Number of absences x in a virtual class 6. 82 86 15 43 9. 74 58 5 90 78 а. -1.59 b. -2.32 с. 2.32 d. 1.59
