Chapter 12 Simple linear regression and correlation - Devore Test Bank

Chapter 12 Simple linear regression and correlation


COMPLETION

1. If y = 2x + 5, then y by when x increases by 1.

ANS: increases, 2

PTS: 1

2. If y = -2x – 8, then the y-intercept is .

ANS: -8

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3. In general, the variable whose value is fixed by the experimenter will be denoted by x and will be called the
independent, predictor, or variable. For fixed x, the second variable will be random; we denote this
random variable and its observed value by Y and y, respectively, and refer to it as the dependent or
variable.

ANS: explanatory, response

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4. A first step in a regression analysis involving two variables is to construct a . In such a plot, each (x,y) is
represented as a point plotted on a two-dimensional coordinate system.

ANS: scatter plot

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, 5. The simple linear regression model is is a random variable assumed to be
distributed, with


ANS: normally, 0,

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6. The estimated regression line or least squares line for the simple linear regression model is the line whose equation is
given by .


ANS:
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7. If then the least squares estimate of the slope coefficient of the true regression line
= .

ANS: -.85

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8. If then the least squares estimate of the slope coefficient of the true
regression line = .

ANS: .5542

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9. If then the least squares estimate of the intercept of the true
regression line = .

ANS: 2

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10. The vertical deviations from the estimated regression line are referred to as the
.

ANS: residuals

PTS: 1

11. When the estimated regression line is obtained via the principle of least squares, the sum of the residuals (i =
1, 3, …….., n) should in theory be .

ANS: zero

, PTS: 1

12. In a simple linear regression problem, the following statistics are given:




Then, the error sum of squares is .

ANS: 2.5

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13. In simple linear regression analysis, the , denoted by , can be interpreted as a measure of how
much variability in y left unexplained by the model - that is, how much cannot be attributed to a linear relationship.

ANS: error sum of squares, SSE

PTS: 1

14. In simple linear regression analysis, a quantitative measure of the total amount of variation in observed y values is
given by the , denoted by .

ANS: total sum of squares, SST

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15. If SSE = 36 and SST = 500, then the proportion of total variation that can be explained by the simple linear regression
model is_ .

ANS: .928

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16. In simple linear regression analysis, SST is the total sum of squares, SSE is the error sum of squares, and SSR is the
regression sum of squares. The coefficient of determination is given by



ANS: SSR, SSE

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17. Since the mean of is an estimator of .

ANS: unbiased

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, 18. In the simple linear regression model Y = the quantity E is a random variable, assumed to be normally
distributed with E( ) = 0, and V( ) = . The estimated standard error of (the least squares estimated of ),

denoted by , is divided by , where .


ANS: s,

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19. In the simple linear regression model the quantity E is a random variable, assumed to be normally
distributed with E( ) = 0 and V( ) = . The estimator has a distribution, because it is a linear
function of independent random variables.

ANS: normal, normal

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20. The assumptions of the simple of the simple linear regression model imply that the standardized variable

has a t distribution with degrees of freedom.

ANS: n - 2

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21. A 100(1 - ) % confidence interval for the slope of the true regression line is .


ANS:

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22. Given that , and n = 15, the 95% confidence interval for the slope of the true regression line
( , ).

ANS: -1.7592, -1.2408

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23. The t critical value for a confidence level of 90% for the slope of the regression line, based on a sample of size 20,
is t = .

ANS: 1.734

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24. In a simple linear regression, the most commonly encountered pair of hypotheses about is
A test of these two hypotheses is often referred to as the .