Practice Quiz Chapter 11

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. What can't be said about the basics of linear regression?

a) The goal of regression is to identify patterns of a relationship. correct incorrect

b) If a pattern is identified it can be extrapolated to make predictions about situations that do not occur in the data correct incorrect

c) Regression allows researchers to make predictions about straight-line relationships correct incorrect

d) Regression allows for prediction between one or more independent variables and a ratio-level dependent variable correct incorrect

e) Regression is not helpful for making predictions about straight-line relationships correct incorrect

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. What is the ordinary least squares method (OLS)?

a) A way to determine which line fits best by seeing which line produces the smallest number when the distance between every case and the line is squared and summed correct incorrect

b) A way to determine which line fits best by seeing which line produces the least number when the distance between all the cases and the line is squared correct incorrect

c) A way to determine which line fits best by seeing which line produces the least number when the distance between every case and the line is summed correct incorrect

d) A way to determine which line fits best by seeing which line produces the smallest number when the distance between every case and the line is divided and summed correct incorrect

e) A way to determine which line fits best by seeing which line produces the largest number when the distance between every case and the line is squared and summed correct incorrect

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. Which of the following is not true about the process to find which line fits the pattern in the data best?

a) Calculate the distance between each case and the line correct incorrect

b) Square each of the distances correct incorrect

c) Take the square root of each of the distances correct incorrect

d) Add together all the results from the previous steps correct incorrect

e) Determine which line is the smallest as it is the best correct incorrect

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. If a scatterplot contains the following distances from the line for the ten cases, then calculate the sum of squared distances from the line: 1,000, 2,000, 0, 4,000, 7,000, -4,000, 3,000, -6,000, 2,000, and 11,000.

a) 256,000 correct incorrect

b) 25,600,000 correct incorrect

c) 25,600 correct incorrect

d) 256,000,000 correct incorrect

e) 2,500 correct incorrect

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. If a scatterplot contains the following distances from the line for the ten cases, then calculate the sum of squared distances from the line: 5,000, 5,000, 1,000, 4,000, 7,000, -6,000, 0, 10,000, 7,000 and -3,000.

a) 310,000,000 correct incorrect

b) 31,000,000 correct incorrect

c) 31,000 correct incorrect

d) 3,100 correct incorrect

e) 3,100,000 correct incorrect

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. Reflecting on your answers from #4 and #5, which is the regression line?

a) Neither fit well correct incorrect

b) The line from #5 correct incorrect

c) The line from #4 correct incorrect

d) Both lines fit well correct incorrect

e) Not enough information exists to answer the question correct incorrect

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One of the following statements about the slope coefficient is not true-which one is it?

a) The slope coefficient provides information about the angle of the regression line correct incorrect

b) The slope coefficient indicates whether an increase in the independent variable is associated with an increase or decrease in the dependent variable correct incorrect

c) The slope coefficient provides information about the magnitude of a relationship between two variables correct incorrect

d) The slope coefficient is denoted by the letter b correct incorrect

e) The slope coefficient is denoted by the letter a correct incorrect

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. The values of the slope coefficient determine a great deal about the line being described. Which of the following cannot be said about this link between the slope coefficient and the line?

a) Lines with positive slope coefficients will be angled upwards from left to right correct incorrect

b) Lines with positive slope coefficients will be angled upwards from right to left correct incorrect

c) The larger the slope coefficient, the closer the line will be to vertical correct incorrect

d) A line with a slope coefficient of 0 will be perfectly horizontal correct incorrect

e) A line with a negative slope coefficient will be angled downwards from left to right correct incorrect

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. Which of the following statements cannot be said about the constant coefficient?

a) The constant coefficient is denoted by the letter b correct incorrect

b) It shows the value on the dependent variable (y) when the value on the independent variable (x) is equal to zero correct incorrect

c) It is the place where the line crosses the vertical axis (y-axis) correct incorrect

d) It is sometimes called the intercept correct incorrect

e) The constant coefficient is denoted by the letter a correct incorrect

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. Once the general pattern of a relationship is identified using a regression line, what two things are necessary for the linear regression prediction equation?

a) The constant and slope averages correct incorrect

b) The constant and slope coefficients correct incorrect

c) The slope coefficient correct incorrect

d) The constant coefficient correct incorrect

e) The stable coefficient correct incorrect

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The chapter frames the discussion about linear regression around the relationship between the length of time an immigrant has spent in the country and their income. If an immigrant has spent 8 years in the country, a equals $20,941.85 and b equals $2,011.63, then what is the annual employment income for an individual in the country for this length of time?

a) $3,705 correct incorrect

b) $37,035 correct incorrect

c) $35,000 correct incorrect

d) $35,005 correct incorrect

e) $3,507 correct incorrect

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The chapter frames the discussion about linear regression around the relationship between the length of time an immigrant has spent in the country and their income. If an immigrant has spent 2 years in the country, a equals $20,941.85 and b equals $2,011.63, then what is the annual employment income for an individual in the country for this length of time?

a) $14,966 correct incorrect

b) $249,660 correct incorrect

c) $37,035 correct incorrect

d) $2,496 correct incorrect

e) $24,966 correct incorrect

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. One of the following statements describing the regression line is false. Which one is it?

a) The regression line best fits the general pattern of the observed relationship correct incorrect

b) The best fitting regression line is the one that minimizes the squared distances between each case and the line correct incorrect

c) A straight line of best fit can be described using a slope coefficient and a constant coefficient correct incorrect

d) The best-fitting regression line is the one that maximizes the squared distances between each case and the line correct incorrect

e) One way to find the regression line is to test different lines until you eventually find the one with the least squared differences from the line correct incorrect

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. If the sum of products is 173,000 and the sum of squares for the independent variable is 86, then what is the slope coefficient?

a) 2,012 correct incorrect

b) 212 correct incorrect

c) 2,102 correct incorrect

d) 21 correct incorrect

e) 2.012 correct incorrect

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. What does it mean if a case has a large residual?

a) The value on the dependent variable is perfectly predicted by the value on the independent variable correct incorrect

b) The regression line is a good fit correct incorrect

c) The value on the independent variable does a poor job of predicting the value on the dependent variable correct incorrect

d) The value on the independent variable does a good job of predicting the value on the dependent variable correct incorrect

e) The value on the dependent variable does a poor job of predicting the value on the independent variable correct incorrect

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. One of the following choices is not part of the simple linear regression equation–which one is it?

a) yi correct incorrect

b) a correct incorrect

c) bxi correct incorrect

d) ei correct incorrect

e) abi correct incorrect

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. How do researchers calculate R2?

a) Dividing the variation in the DV explained by the IV by the total variation in the DV correct incorrect

b) Dividing the variation in the IV explained by the DV by the total variation in the DV correct incorrect

c) Dividing the variation in the IV explained by the DV by the total variation in the IV correct incorrect

d) Dividing the variation in the DV explained by the IV by the total variation in the IV correct incorrect

e) Dividing the variation in the DV by the variation in the IV correct incorrect

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. Which of the following statements cannot be said about the null model?

a) It is the total variation in the dependent variable correct incorrect

b) In the null model the mean of the dependent variable is predicted for every case correct incorrect

c) The null model illustrates a situation in which the null hypothesis is true correct incorrect

d) The null model considers dependent and independent variables correct incorrect

e) The null model does not contain independent variables correct incorrect

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. Calculate the t-statistic for the slope coefficient using the following information: the slope coefficient is $2,011.63 and the standard error is 560.52.

a) 3.59 correct incorrect

b) 359 correct incorrect

c) 0.359 correct incorrect

d) 3,059 correct incorrect

e) 0.0359 correct incorrect

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. Interpret your answer from the question above. What does it mean in the case of this question about the relationship between number of years since immigration and employment income if the critical value for the t-statistic is +-2.31?

a) The slope coefficient equals 0 correct incorrect

b) The alternative hypothesis is false correct incorrect

c) The null hypothesis is true correct incorrect

d) No relationship exists between the two variables correct incorrect

e) A relationship exists between the two variables in the question correct incorrect

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. In simple linear regression, one ratio-level independent variable is used to predict the value on a ratio-level variable.

a) True correct incorrect

b) False correct incorrect

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. In linear regression, the line of best fit is usually defined as the one that maximizes the squared distances of the cases from the line.

a) True correct incorrect

b) False correct incorrect

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. The idea of squaring differences and then summing them is mathematically consistent with many other statistical techniques.

a) True correct incorrect

b) False correct incorrect

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. The line that best fits the pattern of a relationship between variables observed in the data and minimizes the sum of the squared distances between the cases and the line is called a regression line.

a) True correct incorrect

b) False correct incorrect

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. Influential cases significantly affect the location and direction of the regression line.

a) True correct incorrect

b) False correct incorrect

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. It is uncommon for influential cases to have unusual values on one or both variables or an unusual combination of values.

a) True correct incorrect

b) False correct incorrect

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. You want to make sure to include influential cases in your calculations for the line of best fit.

a) True correct incorrect

b) False correct incorrect

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The formula used to describe a regression line is ŷ = a + bx.

a) True correct incorrect

b) False correct incorrect

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. Any straight line may be described using a slope coefficient and a constant coefficient.

a) True correct incorrect

b) False correct incorrect

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. The slope coefficient shows the size of the increase (decrease) in the dependent variable that is associated with a one-unit increase in the independent variable.

a) True correct incorrect

b) False correct incorrect

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. A line with a slope coefficient of 0 will be perfectly horizontal, indicating that there is a perfect relationship between the variables.

a) True correct incorrect

b) False correct incorrect

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. With the constant coefficient, when the independent variable is 0, the dependent variable is also 0.

a) True correct incorrect

b) False correct incorrect

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A "hat" symbol, also known as a caret, is placed over the y in the linear regression equation to denote that the value is a prediction, not the actual value.

a) True correct incorrect

b) False correct incorrect

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. Slope and constant coefficients are always reported in the same units as the independent variable.

a) True correct incorrect

b) False correct incorrect

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. The ability to make predictions using the pattern of a relationship that is observed in sample data is one of the most powerful features of regression.

a) True correct incorrect

b) False correct incorrect

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It is possible to make predictions using y = a + b(x) that are outside the range of the independent variable in the data.

a) True correct incorrect

b) False correct incorrect

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. The formula for the slope coefficient incorporates two elements of the Pearson's correlation coefficient, the sum of products and the sum of squares for the independent variable.

a) True correct incorrect

b) False correct incorrect

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. Finding the constant coefficient relies on the fact a regression line always passes through the point where the means of the two variables intersect.

a) True correct incorrect

b) False correct incorrect

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. The regression line shows the variation in the independent variable that is explained by the dependent variable.

a) True correct incorrect

b) False correct incorrect

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. Like the standard error of a mean or a proportion, the standard error of a regression coefficient can be estimated using only information from the sample.

a) True correct incorrect

b) False correct incorrect