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linear regression and correlation

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1. The linear correlation coefficient of a set of data points is 0.846.
a. Is the slope of the regression line positive or negative? Explain your answer.
b. Determine the coefficient of determination

2. Obtain the linear correlation coefficient
x= 1,1,5,5
y= 1,3,2,4

3. A random sample of 10 students was taken from an introductory statistics class. The following data were obtained, where x denotes height, in inches, and y denotes score on the final exam.
x= 71, 68, 71, 65, 66, 68, 68, 64, 62, 65
y= 87, 96, 66, 71, 71, 55, 83, 67, 86, 60
a. What sort of value of r would you expect to find for these data? Explain your answer.
b. Compute r.

4. What statistic is used to estimate
a. the y- intercept of the population regression line?
b. the slope of the population regression line?

5. Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.
x= 26,27,33,29,29,34,30,40,22
y= 290,305,325,327,356,411,488,554,246

6. Use the size and price data for custom homes from #5
a. compute the standard error of the estimate and interpret your answer.
b. interpret your results from part (a) if the assumptions for regression inferences hold.
c. obtain a residual plot and a normal probability plot of the residuals.
d. decide whether you can reasonably consider Assumptions 1-3 for regression inferences to be met by the variables under consideration. (The answer here is subjective, especially in view of the extremely small sample sizes.)

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