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- August 27, 2018

ANOVA & LEAST SQUARES A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking through the data.

Based on the data we can assume that if the annual income increases then the amount of money spent on car increases too. The relationship between the annual income and amount of money spent looks to be positive and strong which in turn means that the correlation is close to +1.

B. What is the direction of causality in this relationship - i.e. does having a more expensive car make you earn more money, or does earning more money make you spend more on your car? In other words, define one of these variables as your dependent variable (Y) and one as your independent variable (X).

The direction of causality in this relationship looks like earning more money make you spend more on your car. The Dependent variable (Y) is the amount spent on car where as Independent variable (X) is the annual income level.

C. What method do you think would be best for testing the relationship between your dependent and independent variable, ANOVA or regression? Explain your reasoning thoroughly with a discussion of both methods.

The relationship between the dependent and independent variable can be tested by both ANOVA and regression, but regression provides more information about the relationship. ANOVA analyzes mean differences between groups satisfactorily but if there is a continuous variable like age then ANOVA does not provide the desired results while regression does. Regression analysis unlike ANOVA assumes independence, normality and constant variance but in addition the linear relationships between the dependent and independent variables are assumed. (Frederick T. L. Leong & James T. Austin, 2005, p. 300).

D. Go to this calculation page (http://people.hofstra.edu/Stefan_Waner/newgraph/regressionframes.html) and enter in your data in the X and Y columns (dont use commas, enter 8,000 as 8000). Then click on the button "Y=MX+B". Then click on the "graph" button. Write out your equation as calculated, along with your coefficients. Discuss the significance and interpretation of this result, and discuss your graph.

Regression Y = 0.329224x + 3752.6

Regression Coefficient (r) = 0.88895

The graphical representation of the regression shows that there is a positive relationship between the annual income and the amount of money spent on the car. It is observed that with the variation of the income there is variation in the amount spent on the car.

REFERENCES

1) Frederick T. L. Leong & James T. Austin, 2005, p. 300

2) Programme for International Student Assessment, Organization for Economic Co-operation and Development, 2005, p. 166

3) http://mathbits.com/Mathbits/TISection/Statistics2/correlation.htm

Based on the data we can assume that if the annual income increases then the amount of money spent on car increases too. The relationship between the annual income and amount of money spent looks to be positive and strong which in turn means that the correlation is close to +1.

B. What is the direction of causality in this relationship - i.e. does having a more expensive car make you earn more money, or does earning more money make you spend more on your car? In other words, define one of these variables as your dependent variable (Y) and one as your independent variable (X).

The direction of causality in this relationship looks like earning more money make you spend more on your car. The Dependent variable (Y) is the amount spent on car where as Independent variable (X) is the annual income level.

C. What method do you think would be best for testing the relationship between your dependent and independent variable, ANOVA or regression? Explain your reasoning thoroughly with a discussion of both methods.

The relationship between the dependent and independent variable can be tested by both ANOVA and regression, but regression provides more information about the relationship. ANOVA analyzes mean differences between groups satisfactorily but if there is a continuous variable like age then ANOVA does not provide the desired results while regression does. Regression analysis unlike ANOVA assumes independence, normality and constant variance but in addition the linear relationships between the dependent and independent variables are assumed. (Frederick T. L. Leong & James T. Austin, 2005, p. 300).

D. Go to this calculation page (http://people.hofstra.edu/Stefan_Waner/newgraph/regressionframes.html) and enter in your data in the X and Y columns (dont use commas, enter 8,000 as 8000). Then click on the button "Y=MX+B". Then click on the "graph" button. Write out your equation as calculated, along with your coefficients. Discuss the significance and interpretation of this result, and discuss your graph.

Regression Y = 0.329224x + 3752.6

Regression Coefficient (r) = 0.88895

The graphical representation of the regression shows that there is a positive relationship between the annual income and the amount of money spent on the car. It is observed that with the variation of the income there is variation in the amount spent on the car.

REFERENCES

1) Frederick T. L. Leong & James T. Austin, 2005, p. 300

2) Programme for International Student Assessment, Organization for Economic Co-operation and Development, 2005, p. 166

3) http://mathbits.com/Mathbits/TISection/Statistics2/correlation.htm