PART 1

1) In regression, an independent variable is sometimes called a response variable.

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2) The dependent variable is also called the response variable.

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3) There is no relationship between variables unless the data points lie in a straight line.

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4) In regression, there is random error that can be predicted.

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5) Estimates of the slope, intercept, and error of a regression model are found from sample data.

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6) Error is the difference in the actual value and the predicted value.

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7) The regression line minimizes the sum of the squared errors.

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8) The SSE measures the total variability in the independent variable about the regression line.

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9) The SSR indicates how much of the total variability in the dependent variable is explained by the regression model.

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10) The coefficient of determination takes on values between -1 and + 1.

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11) The regression model assumes the errors are normally distributed.

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12) The standard error of the estimate is also called the variance of the regression.

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13) Which of the following equalities is correct?

A) SST = SSR + SSE

B) SSR = SST + SSE

C) SSE = SSR + SST

D) SST = SSC + SSR

E) SSE = Actual Value – Predicted Value

14) If computing a causal linear regression model of Y = a + bX and the resultant r2 is very near zero, then one would be able to conclude that

A) Y = a + bX is a good forecasting method.

B) Y = a + bX is not a good forecasting method.

C) a multiple linear regression model is a good forecasting method for the data.

D) a multiple linear regression model is not a good forecasting method for the data.

E) None of the above

15) The correlation coefficient resulting from a particular regression analysis was 0.25.  What was the coefficient of determination?

A) 0.5

B) -0.5

C) 0.0625

D) There is insufficient information to answer the question.

E) None of the above

16) Which of the following represents the underlying linear model for hypothesis testing?

A) Y = b0 + b1 X + ε

B) Y = b0 + b1 X

C) Y = β0 + β1 X + ε

D) Y = β0 + β1 X

E) None of the above

PART 2

Use the following information to answer questions number 17 and 18. Show how you derive the answer!

Y-bar = 10

X-bar = 7

X-Variance = 13

X and Y Covariance = 15.5

Y = b0 + b1X

17. Calculate the b1

18. Calculate the b0

Use the following information to answer questions 19 to 23

SST = 32.5

SSE = 10.5

SSR = 22

n = 6

k = 1

á = 0.05

19. Calculate the r2

r2 = 1 – SSE/SST = 1 – 10.5 / 32.5 = 1 – 0.32 = 0.67

20. What is the interpretation of your calculated r2?

The coefficient of determination, denoted R² or r² and pronounced “R squared”, is the proportion of the variation in the dependent variable that is predictable from the independent variable.

The coefficient of determination is a measurement used to explain how much variability of one factor can be caused by its relationship to another related factor.

This would indicate that 67% of the variance of the dependent variable being studied is explained by the variance of the independent variable.

21. Calculate the r

r = Square root of r2 = √0.67 = 0.81

22. Calculate the s2

23. Calculate the s

24. Calculate the F-statistics

25. Should we reject the null hypothesis or not? Why?

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