Find the coefficient of correlation between X of Y from the data given Table 5.1. Assume that X and Y are equiprobable random variables. X 1 2 3 4 Y 2 4 8 10 Table 5.1: Values of X and Y
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- Compute the linear correlation coefficient. The linear correlation coefficient for the four pieces of data is2Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is…
- Assume the random variable X has a standard deviation of 4, the random variable Y has a standard deviation of 5 and the two random variables have a correlation of 0.6. What is the covariance of X and Y?Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 13.8 19.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1554.45; Σxy = 274b) Find the equation of the least-squares line. (Round your answers to two decimal places.) ŷ = + x (c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = d) Test the claim that the population correlation coefficient is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t =The correlation coefficient between variables X and Y is 0.62. What does this signify? Question 8Answer a. When Y increases 1, X increases by 0.62 b. When X increases by 1, Y increases by 0.62 c. The variance shared by X and Y is less 20% d. The variance shared by X and Y is 62%
- Sketch a scatter plot and estimate the Pearson correlation . And then Compute the Pearson correlation. X VALUES: 0,2,1,1 | Y VALUES: 4,9,6,9Suppose we have the following paired observations of variables X and Y: X Y 8 0 4 10 12 20 Draw the scatter plot comparing X and Y. Calculate the values of the sample covariance and sample correlation between X and Y. Using this information, how would you characterize the relationship between X and Y ?23. Find the value of the linear correlation coefficient r. Show work. The paired sample data below consists of the temperatures on randomly chosen days and the amount a certain kind of plant grew in millimeters. Temperature 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16
- In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information. x0.241 0.263 3.8 0.261 0.286 0.268 3.5 0.339 0.299 y 1.1 3.3 5.5 7.3 5.0 (a) Make a scatter diagram of the data. Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties. WebAssign. Graphing Too (b) Use a calculator to verify that Ex = 1.957, Ex2 = 0.553, Ey = 29.5, Ey2 = 147.33 and Exy = 8.607. Compute r. (Round your answer to three decimal places.) As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer. O Given our value of r, y should tend to decrease as x increases. O Given our value of r, y should tend to remain constant as x increases.…(b)For which data set is the sample correlation coefficient r equal to -1? CHOOSE ONE: u, v data set w, t data set none of the data sets (m, n data set & x, y data set answer is wrong)A psychologist has calculated the correlation between two variables as 0.9. Which of the following statements is correct? a. The average value of y changes by 0.9 when x is increased by 1. b. The average value of x changes by 0.9 when y is increased by 1. c. The explanatory variable ( x ) explains 0.9 of the variation in the response variable ( y ) d. The explanatory variable ( x ) explains 0.81 of the variation in the response variable ( y )
