Reference no: EM132432532

Question 1: Given the linear correlation coefficient r = 0.543 and the sample size n = 25, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

Question 2: A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.

Question 3: The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters):

Temp 62 76 50 51 71 46 51 44 79

Growth 36 39 50 13 33 33 17 6 16

Find the value of the linear correlation coefficient r.

Question 4: A regression equation can be used to make predictions of the y value corresponding to a particular x value.

Determine whether the following statement is true or false:

The 95% confidence interval for the mean of all values of y for which x = x0 will be wider than the 95% confidence interval for a single y for which x = x0.

Question 5: The paired data below consist of the costs of advertising (in thousands of £) and the number of products sold (in thousands):

Cost 9 2 3 4 2 5 9 10

Number 85 52 55 68 67 86 83 73

Determine the value of the linear correlation coefficient r.

Question 6: Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

Performance 59 63 65 69 58 77 76 69 70 64

Attitude 72 67 78 82 75 87 92 83 87 78

Determine the value of the linear correlation coefficient r.

Question 7: For each of 200 randomly selected cities, a student recorded the number of religious places in the city (x) and the number of homicides in the past decade (y). She calculated the linear correlation coefficient and was surprised to find a strong positive linear correlation for the two variables.

Does this suggest that building new religious places causes an increase in the number of homicides?

Why do you think that a strong positive linear correlation coefficient was obtained?

Explain your answer with reference to the term lurking variable.

Question 8: Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the following number of pairs of data n and the significance level α:

n = 11, α = 0.05

n = 12, α = 0.01

Question 9: For the data below, determine the value of the linear correlation coefficient r between y and x^2.

X 1.2 2.7 4.4 6.6 9.5

Y 1.6 4.7 9.9 24.5 39.0

Question 10: The equation of the regression line for the paired data below is y? = 3x. Find the unexplained variation.

x 2 4 5 6

y 7 11 13 20