# Probability Distribution, Correlation & Regression Analysis

The scatter plot below shows the relationship between the day of a particular month a stock was valued and the price of the stock in dollars. The horizontal axis represents the day of the month. Use this graph to answer the questions below.

Please see the attachment for the scatter plot.

(A) How would you describe the relationship between the day of the month this stock was valued and the price of the stock?

(B) Approximately what was the stock price on day 8?

(C) Would the slope of the "line of best fit" be positive or negative?

2. Suppose we want to determine the (binomial) probability(p) of getting 6 heads in 12 flips of a 2-sided coin. Using the Binomial Probabilities Table in Appendix B of the text, what values of n, x and p would we use to look up this probability, and what would be the probability?

3. For the table that follows, answer the following questions:

x y

1 -3

2 -2

3 -1

4

Would the correlation between x and y in the table above be positive or negative?

Find the missing value of y in the table.

How would the values of this table be interpreted in terms of linear regression?

If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?

4. Answer the following:

If the correlation coefficient is -0.54, what is the sign of the slope of the regression line?

As the correlation coefficient decreases from 0.86 to 0.81, do the points of the scatter plot move toward the regression line, or away from it?

6. Determine whether each of the distributions given below represents a probability distribution and justify your answer.

(A)

x 1 2 3 4

P(x) 3/8 1/12 7/24 1/3

(B)

x 3 6 8

P(x) 2/25 .1 4/5

(C)

x 20 35 40 50

P(x) 0.54 0.12 -0.03 0.37

7. Three socks are selected, one at a time from a clothes drawer containing 6 black, 6 brown and 6 green socks. Let x represent the number of brown socks selected in 3 selections from the drawer.

(A) If this experiment is completed without replacing the socks each time, explain why x is not a binomial random variable.

(B) If this experiment is completed with replacement of the socks each time, explain why x is a binomial random variable

8. You are given the following data.

Number of Absences Final

Grade

0 93

1 93

2 77

3 68

4 65

5 54

Find the correlation coefficient for the data.

Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.

Please see attachment for 7 problems.

© BrainMass Inc. brainmass.com October 25, 2018, 4:30 am ad1c9bdddfhttps://brainmass.com/statistics/regression-analysis/probability-distribution-correlation-regression-analysis-381112

#### Solution Summary

The solution provides step by step method for the calculation of binomial probability, correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.

Normal Probability

12. Find the area under the normal distribution curve to the right of z = -3.24. (Points : 1)

0.499

-0.499

0.999

0.001

13. Use a scatter plot to deternine the relationship between the x values and the y values.

(Points : 1)

No relationship

Nonlinear relationship

Positive linear relationship

Negative linear relationship

14. The average hourly wage of employees of a certain company is $9.83. Assume the variable is normally distributed. If the standard deviation is $4.58, find the probability that a randomly selected employee earns less than $5.43. (Points : 1)

0.313 = 31.3%

0.332 = 33.2%

0.168 = 16.8%

0.345 = 34.5%

15. Find the area under the normal distribution curve between z = -1.34 and z = 2.95. (Points : 1)

0.908

0.088

0.410

0.498

16. Find the equation of the regression line.

(Points : 1)

y = -1.2 + 2.4x

y = 1.2 + 2.4x

y = 2.4 + 1.2x

y = -2.4 + 1.2x

18. Determine whether a correlation coefficient of r = -0.405 is significant at the 5% level for a sample size of 22. (Points : 1)

r is not significant at 5%.

r is significant at 5%.

19. Find the area under the normal distribution curve between z = 1.52 and z = 2.43. (Points : 1)

0.929

0.436

0.493

0.057

6. Use the equation of the regression line to predict y when x = 20.

(Points : 1)

45.5

50

40

48.5

7. Find the area under the normal distribution curve to the right of z = -1.03. (Points : 1)

0.151

-0.349

0.349

0.849

9. Find the value for the correlation coefficient r.

(Points : 1)

-0.073

-0.094

-0.203

-0.149

10. A data set of size 19 has correlation coefficient of r = -0.432. Test the significance of r at the 5% level and at the 1% level. (Points : 1)

r is significant at 5% and at 1%.

r is significant at 5%, but not at 1%.

r is is not significant at 5% or at 1%.

Please see the attachment.

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