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?
