Question 1

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

Accepted Answer

A)  $\hat { \beta } _ { 0 }$ and $\hat { \beta } _ { 1 }$ . 
B)  $\hat { \beta } _ { 0 }$ and $\beta _ { 1 }$ . 
C)  $\beta _ { 0 }$ and $\hat { \beta } _ { 1 }$ . 
D)  $\beta _ { 0 }$ and $\beta _ { 1 }$ . 
A)  $\hat { \beta } _ { 0 }$ and $\hat { \beta } _ { 1 }$ . 
B)  $\hat { \beta } _ { 0 }$ and $\beta _ { 1 }$ . 
C)  $\beta _ { 0 }$ and $\hat { \beta } _ { 1 }$ . 
D)  $\beta _ { 0 }$ and $\beta _ { 1 }$ .

Question 2

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100 000 of population and the average daily sunshine in eight country towns around NSW. These data are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Average daily sunshine (hours) } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \
\hline \text { Skin cancer per } 100000 & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5 \
\hline
\end{array}$$ Draw a scatter diagram of the data and plot the least squares regression line on it.

Accepted Answer

The answer of A medical statistician wanted to examine the...

Question 3

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ a. Determine the least squares regression line.
b. Interpret the value of the slope of the regression line.
c. Determine the standard error of estimate, and describe what this statistic tells you about the regression line.

Accepted Answer

a. @#IMG-DLM& = 4.225 + 8.285x
b. For ea

Question 4

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

Accepted Answer

A) As x increases by 1 unit, y increases by 1 unit, estimated, on average. 
B) As x increases by 1 unit y decreases by (2 -x) units, estimated, on average. 
C) As x increases by 1 unit, y decreases by 1 unit, estimated, on average. 
D) All of these choices are correct. 
A) As x increases by 1 unit, y increases by 1 unit, estimated, on average. 
B) As x increases by 1 unit y decreases by (2 -x) units, estimated, on average. 
C) As x increases by 1 unit, y decreases by 1 unit, estimated, on average. 
D) All of these choices are correct.

Question 5

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

Accepted Answer

A) explained variation. 
B) unexplained variation. 
C) y-intercept in the model. 
D) outliers. 
A) explained variation. 
B) unexplained variation. 
C) y-intercept in the model. 
D) outliers.

Question 6

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

Accepted Answer

A) The coefficient of determination is 1.0. 
B) The coefficient of correlation is 0.0. 
C) The sum of squares for error is 0.0. 
D) The sum of squares for regression is relatively large. 
A) The coefficient of determination is 1.0. 
B) The coefficient of correlation is 0.0. 
C) The sum of squares for error is 0.0. 
D) The sum of squares for regression is relatively large.

Question 7

The symbol for the population coefficient of correlation is:

Accepted Answer

A) r. 
B)  $\rho$ . 
C) r $2$ . 
D)  $\rho ^ { 2 }$ . 
A) r. 
B)  $\rho$ . 
C) r $2$ . 
D)  $\rho ^ { 2 }$ .

Question 8

In order to estimate with 95% confidence a particular value of $y$ for a given value of $x$ in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

Accepted Answer

A) True 
 B)False

Question 9

The standardised residual is defined as:

Accepted Answer

A) residual divided by the standard error of estimate. 
B) residual multiplied by the square root of the standard error of estimate. 
C) residual divided by the square of the standard error of estimate. 
D) residual multiplied by the standard error of estimate. 
A) residual divided by the standard error of estimate. 
B) residual multiplied by the square root of the standard error of estimate. 
C) residual divided by the square of the standard error of estimate. 
D) residual multiplied by the standard error of estimate.

Question 10

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education. The results are as follows. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Use the regression equation to determine the predicted values of y.

Accepted Answer

@#IMG-DLM& : 754.167, 397.500,

Question 11

The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books will cost more money. As an experiment to analyse the claim, a university student visits the bookstore and records the number of pages and the selling price of 12 randomly selected books. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Book } & \text { Number of pages } & \text { Selling price } ( \$ ) \
\hline 1 & 844 & 55 \
\hline 2 & 727 & 50 \
\hline 3 & 360 & 35 \
\hline 4 & 915 & 60 \
\hline 5 & 295 & 30 \
\hline 6 & 706 & 50 \
\hline 7 & 410 & 40 \
\hline 8 & 905 & 53 \
\hline 9 & 1058 & 65 \
\hline 10 & 865 & 54 \
\hline 11 & 677 & 42 \
\hline 12 & 912 & 58 \
\hline
\end{array}$$ Draw a scatter diagram of the data and plot the least squares regression line on it.

Accepted Answer

The answer of The editor of a major academic book...

Question 12

The regression line $\hat { y }$ = 2 + 3x has been fitted to the data points (4,11), (2,7), and (1,5). The residual sum of squares will be 10.0.

Accepted Answer

A) True 
 B)False

Question 13

The quality of oil is measured in API gravity degrees - the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field, who believes that there is a relationship between quality and price per barrel. $$\begin{array} { | c | c | } 
\hline \text { Oil degrees API } & \text { Price per barrel (in } \$ \text { ) } \
\hline 27.0 & 12.02 \
\hline 28.5 & 12.04 \
\hline 30.8 & 12.32 \
\hline 31.3 & 12.27 \
\hline 31.9 & 12.49 \
\hline 34.5 & 12.70 \
\hline 34.0 & 12.80 \
\hline 34.7 & 13.00 \
\hline 37.0 & 13.00 \
\hline 41.0 & 13.17 \
\hline 41.0 & 13.19 \
\hline 38.8 & 13.22 \
\hline 39.3 & 13.27 \
\hline
\end{array}$$ A partial computer output follows.
Descriptive Statistics $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \
\hline \text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \
\hline \text { Frice } & 13 & 12.730 & 0.457 & 0.127 \
\hline
\end{array}$$ Covariances $$\begin{array} { | l | r | r | } 
\hline & \text { Degrees } & \text { Price } \
\hline \text { Degrees } & 21.281667 & \
\hline \text { Price } & 2.026750 & 0.208833 \
\hline
\end{array}$$ Regression Analysis $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \
\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \
\hline
\end{array}$$ se = 0.1314 R2 = 92.46% R2(adjusted) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } 
\hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \mathrm { F } & \mathrm { P } \
\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \
\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \
\hline \text { Total } & 12 & 2.5060 & & & \
\hline
\end{array}$$ a. Determine the standard error of estimate and describe what this statistic tells you.
b. Determine the coefficient of determination and discuss what its value tells you about the two variables.
c. Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

a. @#IMG-DLM& 0.1314. Since the sample mean @#IMG-DLM& = 12.

Question 14

Consider the following data values of variables x and y. $$\begin{array} { | c | c | c | c | c | c | c | } 
\hline x & 3 & 5 & 7 & 9 & 11 & 14 \
\hline y & 7 & 10 & 17 & 20 & 27 & 35 \
\hline
\end{array}$$ Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

Accepted Answer

@#IMG-DLM& 0.990. This means that 99% of

Question 15

A statistician investigating the relationship between the amount of precipitation (in inches) and the number of car accidents gathered data for 10 randomly selected days. The results are presented below. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Predict with 95% confidence the number of accidents that occur when there is 0.40 inches of rain.

Accepted Answer

16.316 ± 4

Question 16

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education. The results are as follows. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Predict with 95% confidence the winnings of a contestant who has 10 years of education.

Accepted Answer

843.333 ±

Question 17

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature of that day noted. Excel regression output given below. $$\begin{array} { | c | c | } 
\hline \text { Coffee sales revenue } & \text { Temperature } \
\hline 6.50 & 25 \
\hline 10.00 & 17 \
\hline 5.50 & 30 \
\hline 4.50 & 35 \
\hline 3.50 & 40 \
\hline 28.00 & 9 \
\hline
\end{array}$$ $\begin{array}{|l|r|c|c|c|r|r|}
\hline \text { SUMMARY OUTPUT } & & \
\hline \text { RegressionStatistios } & & \
\hline \text { Multiple R } & 0.8644 & \
\hline \text { RSquare } & 0.7472 & \
\hline \text { Adjusted RSquare } & 0.6840 & \
\hline \text { Standard Error } & 5.2027 & \
\hline \text { Observations } & 6 & \\hline\
\hline \text { ANOVA } & & & & & & \
\hline & d f & S S & M S & F & \text { Significance } F & \
\hline \text { Regression } & 1 & 320.0617 & 320.0617 & 11.8244 & 0.0263 & \
\hline \text { Residual } & 4 & 108.2716 & 27.0679 & & & \
\hline \text { Total } & 5 & 4283333 & & & & \\hline\
\hline & \text { Coefficient } & \text { StandardError } &{\text { tStat }} & \text { P-value } & \text { Lover 95\% } & {\text { Upper 95\% }} \
\hline \text { Intercept } & 27.7179 & 5.6629 & 4.8946 & 0.0081 & 11.9952 & 43.4406 \
\hline \text { Temperature } & -0.6943 & 0.2019 & -3.4387 & 0.0263 & -1.2549 & -0.1337 \
\hline
\end{array}$ Test the significance of the slope, against a two-tailed alternative, at the 5% level of significance.

Accepted Answer

H₀: β₁ = 0 H_A: β₁ ≠ 0 p-value = 0.0263 α = 0

Question 18

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?

Accepted Answer

A) 0.69. 
B) 0.96. 
C) 96. 
D) -100. 
A) 0.69. 
B) 0.96. 
C) 96. 
D) -100.

Question 19

The standard error of the estimate is the standard deviation of the error variable.

Accepted Answer

A) True 
 B)False

Question 20

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education. The results are as follows. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Predict with 95% confidence the winnings of all contestants who have 10 years of education.

Accepted Answer

843.333 ±

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

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

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

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

The symbol for the population coefficient of correlation is:

In order to estimate with 95% confidence a particular value of $y$ for a given value of $x$ in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

The standardised residual is defined as:

The regression line $\hat { y }$ = 2 + 3x has been fitted to the data points (4,11), (2,7), and (1,5). The residual sum of squares will be 10.0.

Consider the following data values of variables x and y. x 3 5 7 9 11 14 y 7 10 17 20 27 35 Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

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?

The standard error of the estimate is the standard deviation of the error variable.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 15: Simple Linear Regression and Correlation

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

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

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

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

The symbol for the population coefficient of correlation is:

In order to estimate with 95% confidence a particular value of yyy for a given value of xxx in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

The standardised residual is defined as:

The regression line y^\hat { y }y^​ = 2 + 3x has been fitted to the data points (4,11), (2,7), and (1,5). The residual sum of squares will be 10.0.

Consider the following data values of variables x and y. x 3 5 7 9 11 14 y 7 10 17 20 27 35 Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

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?

The standard error of the estimate is the standard deviation of the error variable.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

In order to estimate with 95% confidence a particular value of $y$ for a given value of $x$ in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

The regression line $\hat { y }$ = 2 + 3x has been fitted to the data points (4,11), (2,7), and (1,5). The residual sum of squares will be 10.0.