Question 1

In the first-order model ŷ = 8 + 3x1 +5x2, a unit increase in $x _ { 2 }$ , while holding $x _ { 1 }$ constant, increases the value of $y$ on average by 3 units.

Accepted Answer

A) True 
 B)False

Question 2

Consider the following data for two variables, x and y. $$\begin{array} { | c | c c c c c c c c c c | } 
\hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \
\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \
\hline
\end{array}$$ Use Excel to develop an estimated regression equation of the form ? = b0 +b1x + b2x2..

Accepted Answer

@#IMG-DLM& = 66.799

Question 3

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
where
y
= fourth-year accounting course mark (out of 100). $x _ { 1 }$ = GPA in first three years (range 0 to 12). $x _ { 2 }$ = 1 if student's major is accounting.
= 0 if not. $X _ { 3 }$ = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS $y =$ $$9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$$ . $$\begin{array} { | c | r r c | } 
\hline \text { Predictor } & \text { Coef } & \text { SDev } & T \
\hline \text { Constant } & 9.14 & 7.10 & 1.287 \
x _ { 1 } & 6.73 & 1.91 & 3.524 \
x _ { 2 } & 10.42 & 4.16 & 2.505 \
x _ { 3 } & 5.16 & 3.93 & 1.313 \
\hline
\end{array}$$ S = 15.0 R-Sq = 44.2%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r r r r | } 
\hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \
\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \
\text { Error } & 96 & 21553 & 224.510 & \
\hline \text { Total } & 99 & 38651 & & \
\hline
\end{array}
\end{array}$$ Do these results allow us to conclude at the 1% significance level that grade point average in the first three years is linearly related to fourth-year accounting course mark?

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& @#LAT-DLM& .
Rejection region: |t| >

Question 4

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
where
y
= fourth-year accounting course mark (out of 100). $x _ { 1 }$ = GPA in first three years (range 0 to 12). $x _ { 2 }$ = 1 if student's major is accounting.
= 0 if not. $X _ { 3 }$ = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS $y =$ $9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$ . $$\begin{array} { | c | r r c | } 
\hline \text { Predictor } & \text { Coef } & \text { SDev } & T \
\hline \text { Constant } & 9.14 & 7.10 & 1.287 \
x _ { 1 } & 6.73 & 1.91 & 3.524 \
x _ { 2 } & 10.42 & 4.16 & 2.505 \
x _ { 3 } & 5.16 & 3.93 & 1.313 \
\hline
\end{array}$$ S = 15.0 R-Sq = 44.2%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r r r r | } 
\hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \
\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \
\text { Error } & 96 & 21553 & 224.510 & \
\hline \text { Total } & 99 & 38651 & & \
\hline
\end{array}
\end{array}$$ Do these results allow us to conclude at the 1% significance level that on average accounting majors outperform those whose majors are not accounting or finance?

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& @#LAT-DLM& > 0.
Rejection region: t

Question 5

An economist is analysing the incomes of professionals (physicians, dentists and lawyers). He realises that an important factor is the number of years of experience. However, he wants to know if there are differences among the three professional groups. He takes a random sample of 125 professionals and estimates the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
where
y
= annual income (in $1000). $x _ { 1 }$ = years of experience. $x _ { 2 }$ = 1 if physician.
= 0 if not. $X _ { 3 }$ = 1 if dentist.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS $y =$ $71.65 + 2.07 x _ { 1 } + 10.16 x _ { 2 } - 7.44 x _ { 3 }$ . $$\begin{array} { | c | r r r | } 
\hline \text { Predictor } & \text { Coef } & \text { SDev } & T \
\hline \text { Constant } & 71.65 & 18.56 & 3.860 \
x _ { 1 } & 2.07 & 0.81 & 2.556 \
x _ { 2 } & 10.16 & 3.16 & 3.215 \
x _ { 3 } & - 7.44 & 2.85 & - 2.611 \
\hline
\end{array}$$ S = 42.6 R-Sq = 30.9%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r c c c | } 
\hline \text { Source of Variation } & d f & \text { SS } & M S & F \
\hline \text { Regression } & 3 & 98008 & 32669.333 & 18.008 \
\text { Error } & 121 & 219508 & 1814.116 & \
\hline \text { Total } & 124 & 317516 & & \
\hline
\end{array}
\end{array}$$ Is there enough evidence at the 5% significance level to conclude that income and experience are linearly related?

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& @#LAT-DLM& .
Rejection region: |t| >

Question 6

An indicator variable (also called a dummy variable) is a variable that can assume either one of two values (usually 0 and 1), where one value represents the existence of a certain condition, and the other value indicates that the condition does not hold.

Accepted Answer

A) True 
 B)False

Question 7

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: $y =$ $\beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$ .
Where:
y = number of annual fatalities per shire. $x _ { 1 }$ = number of cars registered in the shire (in units of 10 000). $x _ { 2 }$ = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS $y =$ $69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$ . $$\begin{array} { | c | r r r | } 
\hline \text { Predictor } & \text { Coef } & \text { SDev } & T \
\hline \text { Constant } & 69.7 & 41.3 & 1.688 \
x _ { 1 } & 11.3 & 5.1 & 2.216 \
x _ { 2 } & 7.61 & 2.55 & 2.984 \
x _ { 1 } ^ { 2 } & - 1.15 & 0.64 & - 1.797 \
x _ { 2 } ^ { 2 } & - 0.51 & 0.20 & - 2.55 \
x _ { 1 } x _ { 2 } & - 0.13 & 0.10 & - 1.30 \
\hline
\end{array}$$ S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } 
\hline \text { Source of } & d f & \text { SS } & M S & F \
\text { Variation } & & & & \
\hline \text { Regression } & 5 & 5959 & 1191.800 & 5.181 \
\text { Error } & 29 & 6671 & 230.034 & \
\hline \text { Total } & 34 & 12630 & & \
\hline
\end{array}$$ Test at the 1% significance level to determine whether the $x _ { 1 } ^ { 2 }$ term should be retained in the model.

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& @#LAT-DLM& .
Rejection region: |t| >

Question 8

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: $y =$ $\beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$ .
Where:
y = number of annual fatalities per shire. $x _ { 1 }$ = number of cars registered in the shire (in units of 10 000). $x _ { 2 }$ = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS $y =$ $69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$ . $$\begin{array} { | c | r r r | } 
\hline \text { Predictor } & \text { Coef } & \text { SDev } & \multicolumn{1}{c|} { \text { T } } \
\hline \text { Constant } & 69.7 & 41.3 & 1.688 \
x _ { 1 } & 11.3 & 5.1 & 2.216 \
x _ { 2 } & 7.61 & 2.55 & 2.984 \
x _ { 1 } ^ { 2 } & - 1.15 & 0.64 & - 1.797 \
x _ { 2 } ^ { 2 } & - 0.51 & 0.20 & - 2.55 \
x _ { 1 } x _ { 2 } & - 0.13 & 0.10 & - 1.30 \
\hline
\end{array}$$ S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } 
\hline \text { Source of } & d f & \text { SS } & M S & F \
\text { Variation } & & & & \
\hline \text { Regression } & 5 & 5959 & 1191.800 & 5.181 \
\text { Error } & 29 & 6671 & 230.034 & \
\hline \text { Total } & 34 & 12630 & & \
\hline
\end{array}$$ What is the multiple coefficient of determination? What does this statistic tell you about the model?

Accepted Answer

@#LAT-DLM& 0.472, which means that 47.2%

Question 9

In explaining the amount of money spent on children's toys during Christmas each year, the independent variable 'gender' is best represented by a dummy variable.

Accepted Answer

A) True 
 B)False

Question 10

For the regression equation  $ = 20 + 8 x _ { 1 } + 5 x _ { 2 } + 3 x _ { 1 } x _ { 2 }$ , which combination of $x _ { 1 }$ and $x _ { 2 }$ , respectively, results in the largest average value of y?

Accepted Answer

A)  3 and 5. 
B)  5 and 3. 
C)  6 and 3. 
D)  3 and 6. 
A)  3 and 5. 
B)  5 and 3. 
C)  6 and 3. 
D)  3 and 6.

Question 11

Which of the following is not an advantage of multiple regression as compared with analysis of variance?

Accepted Answer

A)  Multiple regression can be used to estimate the relationship between the dependent variable and independent variables. 
B)  Multiple regression handles qualitative variables better than analysis of variance. 
C)  Multiple regression handles problems with more than two independent variables better than analysis of variance. 
D)  All of the above are advantages of multiple regression as compared with analysis of variance. 
A)  Multiple regression can be used to estimate the relationship between the dependent variable and independent variables. 
B)  Multiple regression handles qualitative variables better than analysis of variance. 
C)  Multiple regression handles problems with more than two independent variables better than analysis of variance. 
D)  All of the above are advantages of multiple regression as compared with analysis of variance.

Question 12

The model  
$= \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ is referred to as a first-order model with two predictor variables with no interaction.

Accepted Answer

A) True 
 B)False

Question 13

Consider the following data for two variables, x and y. $$\begin{array} { | c | c c c c c c c c c c | } 
\hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \
\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \
\hline
\end{array}$$ Use Excel to determine whether there is sufficient evidence at the 1% significance level to infer that the relationship between y, x and $x ^ { 2 }$ in  = 66.799 -7.307x + 0.324x2 is significant.

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& At least one @#LAT-DLM& is not equal

Question 14

In the first-order model  
$= 50 + 25 x _ { 1 } - 10 x _ { 2 } - 6 x _ { 1 } x _ { 2 }$ , a unit increase in $x _ { 2 }$ , while holding $x _ { 1 }$ constant at a value of 3, decreases the value of $y$ on average by 3 units.

Accepted Answer

A) True 
 B)False

Question 15

Consider the following data for two variables, x and y, where x is the age of a particular make of car
and y is the selling price, in thousands of dollars. $$\begin{array} { | c | c c c c c c c c c c | } 
\hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \
\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \
\hline
\end{array}$$ a. Use Excel to develop an estimated regression equation of the form   = b0 +b1x.
b. Interpret the intercept.
c. Interpret the slope.

Accepted Answer

@#IMG-DLM& a. Estimated selling price = 50.144 -2.

Question 16

The following model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ + $\varepsilon$ is used whenever the statistician believes that, on average, y is linearly related to:

Accepted Answer

A)  $x _ { 1 }$ , and the predictor variables do not interact. 
B)  $x _ { 2 }$ , and the predictor variables do not interact. 
C)  $x _ { 1 }$ and the predictor variables do not interact or to $x _ { 2 }$ , and the predictor variables do not interact. 
D)  $x _ { 1 }$ and the predictor variables do not interact and to $x _ { 2 }$ , and the predictor variables do not interact. 
A)  $x _ { 1 }$ , and the predictor variables do not interact. 
B)  $x _ { 2 }$ , and the predictor variables do not interact. 
C)  $x _ { 1 }$ and the predictor variables do not interact or to $x _ { 2 }$ , and the predictor variables do not interact. 
D)  $x _ { 1 }$ and the predictor variables do not interact and to $x _ { 2 }$ , and the predictor variables do not interact.

Question 17

An economist is in the process of developing a model to predict the price of gold. She believes that the two most important variables are the price of a barrel of oil $\left( x _ { 1 } \right)$ and the interest rate $$\left( x _ { 2 } \right)$$ She proposes the first-order model with interaction: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 3 } + \varepsilon$ . A random sample of 20 daily observations was taken. The computer output is shown below.
THE REGRESSION EQUATION IS
$$y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$$
$\begin{array}{|c|rrc|}
\hline \text { Predictor } & \text { Coef } & \text { S2Dev } & T \
\hline \text { Constant } & 115.6 & 78.1 & 1.480 \
x_{1} & 22.3 & 7.1 & 3.141 \
x_{2} & 14.7 & 6.3 & 2.333 \
x_{1} x_{2} & -1.36 & 0.52 & -2.615 \
\hline
\end{array}$
$$\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|rrrr|}
\hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \
\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \
\text { Error } & 16 & 6971 & 435.7 & \
\hline \text { Total } & 19 & 15632 & & \
\hline
\end{array}$ Is there sufficient evidence at the 1% significance level to conclude that the interaction term should be retained?

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& @#LAT-DLM& .
Rejection region: |t| >

Question 18

Consider the following data for two variables, x and y. $$\begin{array} { | c | c c c c c c c c c c | } 
\hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \
\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \
\hline
\end{array}$$ Use Excel to find the coefficient of determination. What does this statistic tell you about this curvilinear model?

Accepted Answer

@#LAT-DLM& 0.747, which means that about

Question 19

The model  $= \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ is referred to as a second-order model with two predictor variables with interaction.

Accepted Answer

A) True 
 B)False

Question 20

Which of the following best describes Stepwise regression?

Accepted Answer

A)  Stepwise regression may involve adding one independent variable at a time. 
B)  Stepwise regression may involve deleting one independent variable at a time. 
C)  Stepwise regression may involve dividing one independent variable at a time. 
D)  Stepwise regression may involve adding or deleting one independent variable at a time. 
A)  Stepwise regression may involve adding one independent variable at a time. 
B)  Stepwise regression may involve deleting one independent variable at a time. 
C)  Stepwise regression may involve dividing one independent variable at a time. 
D)  Stepwise regression may involve adding or deleting one independent variable at a time.

In the first-order model ŷ = 8 + 3x₁ +5x₂, a unit increase in $x _ { 2 }$ , while holding $x _ { 1 }$ constant, increases the value of $y$ on average by 3 units.

Consider the following data for two variables, x and y. x 7 10 3 5 3 10 4 14 5 8 y 35.0 28.5 45.0 45.0 55.0 25.0 37.5 27.5 30.0 27.5 Use Excel to develop an estimated regression equation of the form ? = b₀ +b₁x + b₂x²..

An indicator variable (also called a dummy variable) is a variable that can assume either one of two values (usually 0 and 1), where one value represents the existence of a certain condition, and the other value indicates that the condition does not hold.

In explaining the amount of money spent on children's toys during Christmas each year, the independent variable 'gender' is best represented by a dummy variable.

Which of the following is not an advantage of multiple regression as compared with analysis of variance?

The following model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ + $\varepsilon$ is used whenever the statistician believes that, on average, y is linearly related to:

Consider the following data for two variables, x and y. x 7 10 3 5 3 10 4 14 5 8 y 35.0 28.5 45.0 45.0 55.0 25.0 37.5 27.5 30.0 27.5 Use Excel to find the coefficient of determination. What does this statistic tell you about this curvilinear model?

Which of the following best describes Stepwise regression?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 20: Model Building

In the first-order model ŷ = 8 + 3x1 +5x2, a unit increase in x2x _ { 2 }x2​ , while holding x1x _ { 1 }x1​ constant, increases the value of yyy on average by 3 units.

Consider the following data for two variables, x and y. x 7 10 3 5 3 10 4 14 5 8 y 35.0 28.5 45.0 45.0 55.0 25.0 37.5 27.5 30.0 27.5 Use Excel to develop an estimated regression equation of the form ? = b0 +b1x + b2x2..

An indicator variable (also called a dummy variable) is a variable that can assume either one of two values (usually 0 and 1), where one value represents the existence of a certain condition, and the other value indicates that the condition does not hold.

In explaining the amount of money spent on children's toys during Christmas each year, the independent variable 'gender' is best represented by a dummy variable.

For the regression equation =20+8x1+5x2+3x1x2 = 20 + 8 x _ { 1 } + 5 x _ { 2 } + 3 x _ { 1 } x _ { 2 }=20+8x1​+5x2​+3x1​x2​ , which combination of x1x _ { 1 }x1​ and x2x _ { 2 }x2​ , respectively, results in the largest average value of y?

Which of the following is not an advantage of multiple regression as compared with analysis of variance?

The model =β0+β1x1+β2x2= \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }=β0​+β1​x1​+β2​x2​ is referred to as a first-order model with two predictor variables with no interaction.

In the first-order model =50+25x1−10x2−6x1x2= 50 + 25 x _ { 1 } - 10 x _ { 2 } - 6 x _ { 1 } x _ { 2 }=50+25x1​−10x2​−6x1​x2​ , a unit increase in x2x _ { 2 }x2​ , while holding x1x _ { 1 }x1​ constant at a value of 3, decreases the value of yyy on average by 3 units.

The following model y=β0+β1x1+β2x2y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }y=β0​+β1​x1​+β2​x2​ + ε\varepsilonε is used whenever the statistician believes that, on average, y is linearly related to:

Consider the following data for two variables, x and y. x 7 10 3 5 3 10 4 14 5 8 y 35.0 28.5 45.0 45.0 55.0 25.0 37.5 27.5 30.0 27.5 Use Excel to find the coefficient of determination. What does this statistic tell you about this curvilinear model?

The model =β0+β1x1+β2x2+β3x1x2= \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }=β0​+β1​x1​+β2​x2​+β3​x1​x2​ is referred to as a second-order model with two predictor variables with interaction.

Which of the following best describes Stepwise regression?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

In the first-order model ŷ = 8 + 3x₁ +5x₂, a unit increase in $x _ { 2 }$ , while holding $x _ { 1 }$ constant, increases the value of $y$ on average by 3 units.

Consider the following data for two variables, x and y. x 7 10 3 5 3 10 4 14 5 8 y 35.0 28.5 45.0 45.0 55.0 25.0 37.5 27.5 30.0 27.5 Use Excel to develop an estimated regression equation of the form ? = b₀ +b₁x + b₂x²..

The following model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ + $\varepsilon$ is used whenever the statistician believes that, on average, y is linearly related to: