Practice Quiz Chapter 11

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

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

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

. 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.

. 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.

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

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

. 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?

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

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

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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?

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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?

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

. 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?

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

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

. How do researchers calculate R2?

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

. 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.

. 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?

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

. 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.

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

. 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.

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

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

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

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

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

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

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

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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.

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

. 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.

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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.

. 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.

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

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

. 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.

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