# ANOVA problems

Please see attached file for full problem description.

1) Answer the following questions:

a) If r2 = 0.95, n = 11 and the = 100, what is or ?

b) If r2 = 1, then in (1a) can be shown to have what type of relationship with SST and SSR?

c) What relationship exists between and Y where r2 = 1?

d) What relationship exists between and Y where r2 = 0?

e) Given the following information: r2 = 0.95, n = 10 and k =2 what is the t-value for b1?

f) In (e), you calculated t-value at the 0.05 level of significance; what statistical decision can you make about b1?

2) Answer the following questions:

a) Given the equation: = 10 + 0.69x1; n =10 and r2 = 0.96, write down the p-value for your calculated t-statistic.

b) Calculate the coefficient of correlation from the information in (a). Write the Ho and H1. Then, make a decision about the significance of the coefficient of correlation.

c) What is the in (a)? If SST = 20 in (a), what is SSE? What is SSR?

3) The following regression equation was obtained using the five independent variables.

The regression equation is

sales = - 19.7 - 0.00063 outlets + 1.74 cars + 0.410 income + 2.04 age - 0.034 bosses

Predictor Coef SE Coef T P

Constant -19.672 5.422 -3.63 0.022

outlets -0.000629 0.002638 -0.24 0.823

cars 1.7399 0.5530 3.15 0.035

income 0.40994 0.04385 9.35 0.001

age 2.0357 0.8779 2.32 0.081

bosses -0.0344 0.1880 -0.18 0.864

S = 1.507 R-Sq = 99.4% R-Sq(adj) = 98.7%

Analysis of Variance

Source DF SS MS F P

Regression 5 1593.81 318.76 140.36 0.000

Residual Error 4 9.08 2.27

Total 9 1602.89

(Minitab Software)

a) What percent of the variation is explained by the regression equation?

b) What is the standard error of regression?

c) What is the critical value of the F-statistic?

d) What sample size is used in the print out?

e) What is the variance of the slope coefficient of income?

f) Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero.

g) Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating outlets and bosses?

4) A metropolitan bus system sampler's rider counts on one of its express commuter routes for a week. Use the following data to establish whether rider ship is evenly balanced by day of the week. Let = 0.05.

Day Monday Tuesday Wednesday Thursday Friday

Rider Count 10 34 21 57 44

1. Is the 2 value significant at 5% level of significant?

2. Write the conclusion for this question

5) Computer output:

Coefficients Std. Error t-Stat P-value

Intercept 729.8665 169.25751 4.3121659 0.0010099

Price -10.887 3.4952397 -3.1148078 0.0089406

Advertising 0.0465 0.0176228 2.6386297 0.0216284

ANOVA

df SS MS F Significance F

Regression 2 12442.8 6221.4 37.56127994 0.00000683

Residual 12 1987.6 165.63333

Total 14 14430.4

Se =12.86986 R-sq = 0.862263 R-sq(adj) = 0.8393068

a) Write and interpret the multiple regression equation.

b) Does the model with Price and Advertising contribute to the prediction of Y? Use a 0.05 significance level.

c) Which independent variable appears to be the best predictor of sales? Explain.

d) What is the number of observations used in this study?

e) Assuming that the coefficient on Advertising has Ha: B1 > 0, what statistical decision should be made at 5% level.

f) What is the standard error of estimate? Can you use this statistic to assess the model's fit? If so, how?

g) What is the coefficient of determination, and what does it tell you about the regression model?

h) What is the coefficient of determination, adjusted for degrees of freedom? What do this statistic and the statistic referred to in part (g) tell you about how well this model fits that data.

i) Test the overall utility of the model. What does the p-value of the test statistic tell you?

6) The Acme corp. wished to predict maintenance costs per year on its factory equipment by knowledge of the equipment's age. The following data was collected which yielded the regression equation: (see the printout)

Age Maintenance Costs

6 920

7 1810

1 230

3 400

6 1260

a) What is the point estimate of maintenance cost for a machine that is 3 years old?

b) Determine the 4 missing values in the printout given below.

SUMMARY OUTPUT

Regression Statistics

Multiple R ( )

R Square 0.843041

Adjusted R Square 0.790722

Standard Error ( )

Observations 5

ANOVA

df SS MS F Significance F

Regression 1 ( ) 1394491 16.1133 0.027751

Residual 3 259628.6 86542.86

Total 4 1654120

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -158.095 299.9618 -0.52705 0.634646 -1112.71 796.5172 -1112.71 796.5172

X Variable 1 235.2381 58.60239 ( ) 0.027751 48.73913 421.7371 48.73913 421.7371

a) Predict the value of when X = 16

b) What is the maximum and minimum value for r?

c) If r2 is 1 what does it mean?

d) What is lower limit and upper limit of r2?

e) Complete table and sum each column

7) A large hotel purchased 200 new color televisions several months ago: 80 of one brand and 60 of each of two other brands. Records were kept for each set as to how many service calls were required, resulting in the table that follows.

Number of

Service Calls TV Brand Total

Sony Toshiba Sanyo

None 8 15 18 41

One 30 55 12 97

Two or more 22 10 30 62

Total 60 80 60 200

Assume the TV sets are random samples of their brands. With 5% risk of Type I error, test for an association between TV brand and the number of service calls.

1. Is the value significant at 5% level of significant?

2. Write the conclusion for this question

8) For n = 6 data points, the following quantities have been calculated:

xy = 400 x = 40 y = 76 x2 = 346 y2 = 1160

(a) Determine the least squares regression line.

(b) Determine the standard error of estimate.

(c) Construct the 95% confidence interval for the mean of y when x = 7.0.

(d) Construct the 95% confidence interval for the mean of y when x = 9.0.

(e) Compared the width of the confidence interval obtained in part (c) with that obtained in part (d). Which is wider and why?

#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here.