# Correlation, Regression and ANOVA problems

(See attached files for full problem descriptions)

Problems One

The analysis of variance technique is a method for

a. comparing three or more means. b. comparing F distributions.

c. measuring sampling error. d. none of the above.

A treatment is

a. a normal population. b. the explained population.

c. a source of variation. d. the amount of random error.

In a one-way ANOVA, k refers to the

a. number of observations in each column. b. the number of treatments.

c. the total number of observations. d. none of the above.

The F distribution is

a. a continuous distribution. b. based on two sets of degrees of freedom.

c. never negative. d. all of the above

In an ANOVA test there are 5 observations in each of three treatments. The degrees of freedom in the numerator and denominator respectively are:

a. 2, 4 b. 3, 15 c. 3, 12 d. 2, 12

Which of the following assumptions is not a requirement for ANOVA?

a. dependent samples b. normal populations

c. equal population variances d. independent samples

The mean square error term (MSE) is the

a. estimate of the common population variance. b. estimate of the population means.

c. estimate of the sample standard deviation. d. treatment variation.

In a one-way ANOVA, the null hypothesis indicates that the treatment means

a. are all the same or from equal populations. b. are not from the same populations.

c. in at least one pair of means are the same. d. are all different.

The appropriate test statistic for comparing two sample variances to find out if they came from the same or equal populations is the

a. t distribution. b. z distribution.

c. F distribution. d. binomial distribution.

What is the probability for an F of more than 6.55 with 3 degrees of freedom in the numerator and 10 in the denominator?

a. 0.025 b. 0.001

c. 0.01 d. 0.05

Record your answer in the space provided. Show essential calculations.

___________________________________________________________________________

Use Single Factor ANOVA in Excel. See Ch 12 in the Excel Resources link on your website..

Youngsville Northeast Corry

2.2 2.3 0.9

1.2 1.5 0.8

1.9 1.2 1.1

3.1 1.4 1.2

1.8 2.2 0.7

1.5

The County Executive for Monroe County is concerned about the response time for the three fire companies in the county. Samples of the response times (in minutes) for each company follow. At the 0.05 significance level is there a difference in the mean response time?

a. State the null and alternate hypotheses.

H0: ____________________________________________________________________

H1: ____________________________________________________________________

b. State the decision rule.

___________________________________________________________________________

c. Compute the value of the test statistic.

d. What is your decision regarding the null hypothesis? Interpret the result.

___________________________________________________________________________

Brand Weeks of Wear

A 3 4 6 3 4

B 2 3 2 5 2

C 5 7 5 4 6

A dentist is trying to decide if there is a difference in the number of weeks three different toothbrushes last. Fifteen patients were randomly assigned to three brands of toothbrushes and the number of weeks that the toothbrushes lasted is given. At the 0.05 significance level, is there a difference in the mean length of time the toothbrushes lasted?

a. State the null and alternate hypotheses.

H0: ______________________________________________________________________

H1: ______________________________________________________________________

b. State the decision rule.

___________________________________________________________________________

c. Compute the value of the test statistic.

d. What is your decision regarding the null hypothesis? Interpret the result.

___________________________________________________________________________

Problems 2

Which of the following statements is not correct regarding the coefficient of correlation.

a. It can range from 1 to 1.

b. Its square is the coefficient of determination.

c. It measures the percent of variation explained.

d. It is a measure of the association between two variables.

The coefficient of determination

a. is usually written as r2.

b. cannot be negative.

c. is the square of the coefficient of correlation.

d. all of the above.

The coefficient of correlation was computed to be 0.60. This means

a. the coefficient of determination is .

b. as X increase Y decreases.

c. X and Y are both 0.

d. as X decreases Y decreases.

Which of the following is a stronger correlation than 0.54?

a. 0.67 b. 0.45

c. 0.0 d. 0.45

A regression equation is used to

a. measure the association between two variables.

b. estimate the value of the dependent variable based on the independent variable.

c. estimate the value of the independent variable based on the dependent variable.

d. estimate the coefficient of determination.

A regression equation was computed to be Y= = 35 + 6X. The value of the 35 indicates that

a. the regression line crosses the Y-axis at 35.

b. the coefficient of correlation is 35.

c. the coefficient of determination is 35.

d. an increase of one unit in X will result in an increase of 35 in Y.

The standard error of estimate

a. is a measure of the variation around the regression line.

b. cannot be negative.

c. is in the same units as the dependent variable.

d. all of the above.

The variable plotted on the horizontal or X-axis in a scatter diagram is called the

a. scatter variable. b. independent variable.

c. dependent variable. d. correlation variable.

The least squares principle means that

a. . b. is maximized.

c. is minimized. d. is minimized.

If all the points are on the regression line, then

a. the value of b is 0. b. the value of a is 0.

c. the correlation coefficient is 0. d. the standard error of estimate is 0.

Record your answers in the space provided. Use the Regression function in Excel.

Week Sales

staff Cars

sold

1 5 53

2 5 47

3 7 48

4 4 50

5 10 58

6 12 62

7 3 45

8 11 60

Tem Rousos, president of Rousos Ford, believes there is a relationship between the number of new cars sold and the number of sales people on duty. To investigate he selects a sample of eight weeks and determines the number of new cars sold and the number of sales people on duty for that week.

b. Determine the coefficient of correlation.

c. Determine the coefficient of determination. Comment on the strength of the association between the two variables.

___________________________________________________________________________

___________________________________________________________________________

d. Determine the regression equation.

e. Interpret the regression equation. Where does the equation cross the Y-axis? How many additional cars can the dealer expect to sell for each additional salesperson employed?

__________________________________________________________________

__________________________________________________________________

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The solution gives answers to multiple choice questions on correlation, regression, ANOVA and testing of hypothesis problems.