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Chapter 13 Correlation and Linear Regression, Exams of Statistics

PJA SchoolStatistics

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

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Chapter 13 - Correlation and Linear Regression
Chapter 13
Correlation and Linear Regression
True / False Questions
1.A scatter diagram is a graph that portrays the correlation between a dependent variable and
an independent variable.
TrueFalse
2.An economist is interested in predicting the unemployment rate based on gross domestic
product. Since the economist is interested in predicting unemployment, the independent
variable is gross domestic product.
TrueFalse
3.Correlation analysis is a statistical technique used to measure the strength of the
relationship between two variables.
TrueFalse
4.The strength of the correlation between two variables depends on the sign of the coefficient
of correlation.
TrueFalse
5.The coefficient of determination is the proportion of total variation in Y that is explained by
X.
TrueFalse
6.The coefficient of determination is the square root of the coefficient of correlation.
TrueFalse
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Chapter 13

Correlation and Linear Regression

True / False Questions

  1. A scatter diagram is a graph that portrays the correlation between a dependent variable and an independent variable. True False
  2. An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product. True False
  3. Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables. True False
  4. The strength of the correlation between two variables depends on the sign of the coefficient of correlation. True False
  5. The coefficient of determination is the proportion of total variation in Y that is explained by X. True False
  6. The coefficient of determination is the square root of the coefficient of correlation. True False
  1. The standard error of estimate measures the accuracy of a prediction. True False
  2. If the coefficient of determination is expressed as a percent, its value is between 0% and 100%. True False
  3. One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value. True False
  4. The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y. True False
  5. The values of a and b in the regression equation are called the regression coefficients. True False
  6. The hypothesis to test the slope of a regression equation is H 0 :  = 0. True False
  7. The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X. True False
  8. In regression analysis, error is defined as ( - Y ). True False
  1. What is the range of values that the coefficient of determination can assume? _____ and
  1. A random sample of 15 homes that recently sold is obtained. The correlation between the area of the home, in square feet, and the selling price is 0.40. We want to test the null hypothesis that the correlation in the population is less than or equal to zero versus the alternate that it is greater than zero. The rejection region will fall in the ________ tail of a t distribution.
  1. If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases? ___________
  1. Perfect correlation means that the scatter diagram will appear as a _____________________.
  1. What is the proportion of explained variation called? ________________

Short Answer Questions

  1. What is the value of the correlation coefficient if there is perfect correlation?

Fill in the Blank Questions

  1. If the correlation between sales and advertising is +0.6, what percent of the variation in sales can be attributed to advertising? ______
  1. A chart that shows the relationship between a dependent variable and an independent variable is called a ______________________.
  1. What is the technique used to predict or estimate the value of the dependent variable Y based on a selected value of an independent variable X called?
  1. What principle minimizes the sum of the squares of the vertical deviations about the line?
  1. What do the coefficient of correlation and the slope of the regression line always have in common? __________________
  1. What is the best model to describe a linear relationship between two variables?
  1. The standard error of the estimate measures the scatter or dispersion of the observed values around a ___________________.
  1. Approximately what percent of the values lie within two standard errors of the regression line? ________

Multiple Choice Questions

  1. What is the chart called when the paired data (the dependent and independent variables) are plotted? A. Scatter diagram B. Bar chart C. Pie chart D. Histogram
  2. What is the variable used to predict the value of another called? A. Independent variable B. Dependent variable C. Correlation variable D. Variable of determination
  3. Which of the following statements regarding the coefficient of correlation is true? A. It ranges from 0.0 to +1.0 inclusive. B. It tests for a relationship between two variables. C. A value of 0.00 indicates two variables are related. D. It is calculated as the square of the slope.
  1. What does a coefficient of correlation of 0.70 infer? A. Almost no correlation because 0.70 is close to 1. B. 70% of the variation in one variable is explained by the other C. Coefficient of determination is 0. D. Coefficient of nondetermination is 0.
  2. What is the range of values for a coefficient of correlation? A. 0 to +1. B. -3 to +3 inclusive C. -1.0 to +1.0 inclusive D. Unlimited range
  3. The Pearson product-moment correlation coefficient, r , requires that variables are measured with: A. An interval or ratio scale. B. An ordinal or ratio scale. C. A nominal or ordinal scale. D. A nominal or ratio scale.
  4. If the correlation between two variables is close to one, the association is A. significant. B. moderate. C. insignificant. D. none.
  5. If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y? A. Not related B. Dependent on each other C. Highly related D. X causes Y
  1. If we reject the null hypothesis that tests a population correlation coefficient, what can we conclude about the correlation in the population? A. It is zero B. It could be zero C. It is not zero D. It equals the computed sample correlation
  2. A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what is the computed value of the test statistic? A. 1. B. 2. C. 2. D. 3.
  3. In the regression equation, what does the letter " a " represent? A. Y intercept B. Slope of the line C. Any value of the independent variable that is selected D. Error
  4. In the regression equation, what does the letter " b " represent? A. Y intercept B. Slope of the line C. Any value of the independent variable that is selected D. Value of Y when X = 0
  5. In the regression equation, what does the letter " X " represent? A. Y intercept B. Slope of the line C. The independent variable D. The dependent variable
  1. In the regression equation, what does the letter " Y " represent? A. Y intercept B. Slope of the line C. The independent variable D. The dependent variable
  2. What is the null hypothesis to test the significance of the slope in a regression equation? A. H 0 :  = 0 B. H 0 :   0 C. H 0 :   0 D. H 0 :   0
  3. What is the test statistic to test the significance of the slope in a regression equation? A. z-statistic B. F-statistic C. t-statistic D. -statistic
  4. What are the degrees of freedom used to test the significance of the slope in a regression equation? A. n - 1 B. n - 2 C. n - 1, n - 2 D. (n - 1)(n - 2)
  5. What is the alternate hypothesis to test the significance of the slope in a regression equation? A. H 1 :  = 0 B. H 1 :   0 C. H 1 :   0 D. H 1 :   0
  1. Given the least squares regression equation, Ŷ = 1,202 + 1,133 X , when X = 3, what does Ŷ equal? A. 5, B. 8, C. 4, D. 4,
  2. What is the general form of the regression equation? A. Ŷ= ab B. C. D. Ŷ= abX
  3. Which of the following are true assumptions underlying linear regression? 1) For each value of X , there is a group of Y values which is normally distributed. 2) The means of these normal distributions of Y values all lie on the regression line. 3) The standard deviations of these normal distributions are equal. A. Only (1) B. Only (2) C. Only (3) D. All of them
  4. Based on the regression equation, we can A. predict the value of the dependent variable given a value of the independent variable. B. predict the value of the independent variable given a value of the dependent variable. C. measure the association between two variables. D. measure cause and effect.
  5. Which of the following is true about the standard error of estimate? A. It is a measure of the accuracy of the prediction B. It is based on squared vertical deviations between Y and X C. It can be negative D. It is calculated using the regression mean square
  1. If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate? A. - B. + C. 0 D. Infinity
  2. In the least squares equation, Ŷ = 10 + 20 X the value of 20 indicates A. the Y intercept increases by 20 units for each unit increase in X. B. that Y increases by 20 units for each unit increase in X. C. that X increases by 20 units for each unit increase in Y. D. the error in prediction.
  3. In the equation Ŷ = a + bX , what is Ŷ? A. Slope of the line B. Y intercept C. Predicted value of Y , given a specific X value D. Value of Y when X = 0
  4. Assume the least squares equation is Ŷ = 10 + 20 X. What does the value of 10 in the equation indicate? A. Y intercept B. X increases by 10 for each unit increase in Y C. Y increases by 10, for each unit increase in X D. Error
  5. What is the variable used to predict another variable called? A. Independent variable B. Dependent variable C. Important variable D. Causal variable
  1. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. What is the independent variable? A. Salesperson B. Number of contacts C. Amount of sales D. Sales manager
  2. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results: What is the Y -intercept of the linear equation? A. -12. B. 2. C. -1. D. 12.
  1. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results: What is the slope of the linear equation? A. -12. B. 2. C. -1. D. 12.
  2. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results: What is the standard error of the slope? A. -0. B. 6. C. -12. D. 12.
  1. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression ANOVA shows the following results: What is the value of the coefficient of correlation? A. 0. B. 0. C. 0. D. 9.
  2. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression ANOVA shows the following results: What is the value of the coefficient of determination? A. 9. B. 0. C. 0. D. 0.
  1. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results = 33.4. = 2814.4. The 95% confidence interval for 30 calls is A. 55.8, 51. B. 51.4, 55. C. 46.7, 60. D. 31.1, 76.