Deck 18: Simple Linear Regression and Correlation

Question 1

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

Answer 1

C

Question 2

The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The sum of the squared residuals will be:

Answer 2

D

Question 3

Which of the following statements best describes correlation analysis in a simple linear regression?

Answer 3

B

Question 4

Given a specific value of x and confidence level, which of the following statements is correct?

Question 5

If an estimated regression line has a y-intercept of 10 and a slope of -5, then when x = 0, the estimated value of y is:

Question 6

Given that the sum of squares for error is 50 and the sum of squares for regression is 140, the coefficient of determination is:

Question 7

The Spearman rank correlation coefficient must be used to determine whether a relationship exists between two variables when:

Question 8

The symbol for the population coefficient of correlation is:

Question 9

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

Question 10

In regression analysis, if the coefficient of determination is 1.0, then:

Question 11

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Question 12

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32. The standard error of estimate was:

Question 13

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is:

Question 14

The following sums of squares are produced: $\Sigma$ (y_i-(y-bar))² = 250, $\Sigma$ (y_i-(y_i-hat))² = 100, $\Sigma$ ((y_i-hat)-(y-bar))² = 150
The percentage of the variation in y that is explained by the variation in x is: $\begin{array}{|l|l|}\hline\text { A. } & 60 \% \\\hline \text { B. } & 75 \% \\\hline \text { C. } & 40 \% \\\hline \text { D. } & 50 \% \\\hline\end{array}$

Question 15

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

Question 16

In simple linear regression, most often we perform a two-tail test of the population slope to determine whether there is sufficient evidence to infer that a linear relationship exists. Which of the following best describes the null and alternative hypotheses needed for a test of significance?

Question 17

If the coefficient of correlation is −0.50, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

Question 18

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

Question 19

The symbol for the sample coefficient of correlation is:

Question 20

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85?

Question 21

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line = 75 +6x. This implies that if $800 is spent on advertising, then the predicted amount of sales (in dollars) is:

Question 22

The smallest value that the standard error of estimate can assume is:

Question 23

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

Question 24

Given the data points (x,y) = (3,3), (4,4), (5,5), (6,6), (7,7), the least squares estimates of the y-intercept and slope are respectively:

Question 25

Of the values of the coefficient of determination listed below, which one implies the greatest value of the sum of squares for regression, given that the total variation in y is 1800?

Question 26

When all the actual values of y and the predicted values of y are equal, the standard error of estimate will be:

Question 27

In order to estimate with 95% confidence the expected value of y in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

Question 28

A regression analysis between sales (in $1000) and advertising (in $) yielded the least squares line = 80 000 + 5x. This implies that an:

Question 29

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

Question 30

Which of the following techniques is used to predict the value of one variable on the basis of other variables?

Question 31

In testing the hypotheses: , the Spearman rank correlation coefficient in a sample of 50 observations is 0.389. The value of the test statistic is:

Question 32

Which of the following statements best describes why a linear regression is also called a least squares regression model?

Question 33

If the standard error of estimate = 15 and n = 12, then the sum of squares for error, SSE, is:

Question 34

A regression analysis between height y (in cm) and age x (in years) of 2 to 10 years old boys yielded the least squares line y-hat = 87 + 6.5x. This implies that by each additional year height is expected to:

Question 35

Which of the following statistics and procedures can be used to determine whether a linear model should be employed?

Question 36

In regression analysis, if the coefficient of correlation is -1.0, then:

Question 37

The standardised residual is defined as:

Question 38

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation?

Question 39

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

Question 40

The standard error of estimate, , is given by:

Question 41

In regression analysis, the coefficient of determination, , measures the amount of variation in y that is:

Question 42

If cov(X,Y) = -350, s_x² = 900 and s_y² = 225, then the coefficient of determination is: $\begin{array}{|l|l|}\hline\text { A. } & 0.8819 \\\hline \text { B. } & 0.7778 . \\\hline \text { C. } & -0.0017 \\\hline \text { D. } & 0.0017 . \\\hline\end{array}$

Question 43

When the variance, , of the error variable is a constant no matter what the value of x is, this condition is called:

Question 44

The standard error of estimate, , is a measure of:

Question 45

Which of the following statements best describes the slope in the simple linear regression model?

Question 46

Which of the following best describes the y-intercept in the simple linear regression model?

Question 47

Which of the following best describes if we want to test for a linear relationship between x and y, in regression analysis?

Question 48

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

Question 49

In a regression problem the following pairs (x,y) are given: (1,2), (2.5,2), (3,2), (5,2) and (5.3,2). This indicates that the:

Question 50

Which of the following is not a required condition for the error variable in the simple linear regression model?

Question 51

In simple linear regression, the coefficient of correlation r and the least squares estimate of the population slope :

Question 52

When the sample size n is greater than 30, the Spearman rank correlation coefficient is approximately normally distributed with:

Question 53

The least squares method requires that the variance of the error variable is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

Question 54

In the first-order linear regression model, the population parameters of the y-intercept and the slope are estimated by:

Question 55

Which of the following best describes the coefficient of determination?

Question 56

In a regression problem, if the coefficient of determination is 0.95, this means that:

Question 57

Which of the following best describes the residuals in regression analysis?

Question 58

If a simple linear regression model has no y-intercept, then:

Question 59

In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: = 2250, = 10, = 50, = 75 The least squares estimates of the slope and y-intercept are respectively:

Question 60

The Pearson coefficient of correlation r equals 1 when there is/are no:

Question 61

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

Question 62

In developing a 90% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 15, the appropriate table value would be 1.761.

Question 63

Regardless of the value of x, the standard deviation of the distribution of y values about the regression line is supposed to be constant. This assumption of equal standard deviations about the regression line is called multicollinearity.

Question 64

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is satisfied, the condition is called homoscedasticity.

Question 65

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 100%.

Question 66

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

Question 67

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of the estimate will be 1.0.

Question 68

If the sum of squared residuals is zero, then the:

Question 69

The least squares method for determining the best fit minimises:

Question 70

In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $\rho$ , equals zero.

Question 71

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is violated, the condition is called heteroscedasticity.

Question 72

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be:

Question 73

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

Question 74

The value of the sum of squares for regression, SSR, can never be smaller than 1.

Question 75

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

Question 76

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Question 77

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

Question 78

On the least squares regression line Estimated y= 2 - 3x, the predicted value of y equals: $\begin{array}{|l|l|}\hline A.& -1.0~ when~ x=-1.0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\hline B.& 1.0~ when~ x=1.0.\\\hline C.& 5.0~ when~ x=-1.0.\\\hline D.& 5.0~ when~ x=1.0.\\\hline \end{array}$

Question 79

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate, $S _ { \varepsilon }$ , will be 0.0.

Question 80

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?