Question 1

In general, to represent a nominal independent variable that has n possible categories, we would create n dummy variables.

Accepted Answer

A) True 
 B)False

Question 2

The owner of an air conditioner business wants to investigate the relationship between the weekly number of air conditioners sold, temperature and the seasons of the year.
A random sample of 14 weeks is taken, with the average temperature of that week (in degrees Celsius) and the quarter from which that week belonged, noted.
There are three indicator variables, March, September and December.
Excel is used to generate the following multiple linear regression output. \(\begin{array}{|l|r|r|r|r|r|c|}
\hline \text { SUMMARY OUTPUT } & \
\hline \text { Regression Statistics } & \
\hline \text { Multiple R } & 0.99 \
\hline \text { R Square } & 0.97 \
\hline \text { Adjusted RSquare } & 0.96 \
\hline \text { Standard Error } & 4.54 \
\hline \text { Observations } & 14.00 \
\hline\
\hline \text { ANOVA }\
\hline &{\text { df }} &{SS} &MS & F& {\text { Significance }} \
\hline \text { Regression } & 4.00 & 6999.27 & 1749.82 & 84.86 & 0.00 \
\hline \text { Residual } & 9.00 & 185.58 & 20.62 & & \
\hline \text { Total } & 13.00 & 7184.86 & & & \
\hline\
\hline & \text { Coefficients } & \begin{array}{c}
\text { Standard } \
\text { Error }
\end{array} & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}
\text { Upper } \
95 \%
\end{array} \
\hline \text { Intercept } & -17.94 & 8.54 & -2.10 & 0.07 & -37.27 & 1.38 \\hline \text { Temperature } & 1.00 & 0.35 & 2.84 & 0.02 & 0.20 & 1.79 \
\hline \text { March } & 1.01 & 4.60 & 0.22 & 0.83 & -9.39 & 11.40 \
\hline \text { September } & 7.22 & 5.58 & 1.29 & 0.23 & -5.40 & 19.84 \
\hline \text { Deomber } & 27.87 & 6.55 & 4.26 & 0.00 & 13.06 & 42.68 \
\hline
\end{array}\) Using the p-values from Excel, state which of the quarters are statistically significant at α of 5%.

Accepted Answer

Only Decem

Question 3

The model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ + $\varepsilon$ is referred to as a:

Accepted Answer

A)  first-order model with two predictor variables with no interaction. 
B)  first-order model with two predictor variables with interaction. 
C)  second-order model with three predictor variables with no interaction. 
D)  second-order model with three predictor variables with interaction. 
A)  first-order model with two predictor variables with no interaction. 
B)  first-order model with two predictor variables with interaction. 
C)  second-order model with three predictor variables with no interaction. 
D)  second-order model with three predictor variables with interaction.

Question 4

A regression analysis involving 40 observations and five independent variables revealed that the total variation in the dependent variable y is 1080 and that the mean square for error is 30.
Create the ANOVA table.

Accepted Answer

The answer of A regression analysis involving 40 observations and...

Question 5

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 $y =$ $69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$ . $$\begin{array} { | c | r r c | } 
\hline \text { Predictor } & \text { Coef } & \text { SiDev } & T \
\hline \text { Constant } & 69.7 & 41.3 & 1.688 \
x _ { 1 } & 11.3 & 5.1 & 2.216 \
x _ { 2 } & 7.61 & 2.55 & 2.984 \
x _ { 1 } ^ { 2 } & - 1.15 & 0.64 & - 1.797 \
x _ { 2 } ^ { 2 } & - 0.51 & 0.20 & - 2.55 \
x _ { 1 } x _ { 2 } & - 0.13 & 0.10 & - 1.30 \
\hline
\end{array}$$ S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } 
\hline \begin{array} { l } 
\text { Source of } \
\text { Variation }
\end{array} & d f & \text { SS } & M S & F \
\hline \text { Regression } & 5 & 5959 & 1191.800 & 5.181 \
\text { Error } & 29 & 6671 & 230.034 & \
\hline \text { Total } & 34 & 12630 & & \
\hline
\end{array}$$ Test at the 1% significance level to determine whether the interaction term should be retained in the model.

Accepted Answer

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

Question 6

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 $y =$ $115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$ . $$\begin{array} { | c | r r c | } 
\hline \text { Predictor } & \text { Coef } & \text { SiDev } & T \
\hline \text { Constant } & 115.6 & 78.1 & 1.480 \
x _ { 1 } & 22.3 & 7.1 & 3.141 \
x _ { 2 } & 14.7 & 6.3 & 2.333 \
x _ { 1 } x _ { 2 } & - 1.36 & 0.52 & - 2.615 \
\hline
\end{array}$$ S = 20.9 R-Sq = 55.4%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r r r c | } 
\hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \
\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \
\text { Error } & 16 & 6971 & 435.7 & \
\hline \text { Total } & 19 & 15632 & & \
\hline
\end{array}
\end{array}$$ Interpret the coefficient $b _ { 1 }$ .

Accepted Answer

@#IMG-DLM& = 22.3; as the price of a bar

Question 7

In explaining starting salaries for graduates of computer science programs, which of the following independent variables would not be adequately represented with a dummy variable?

Accepted Answer

A)  Grade point average. 
B)  Gender. 
C)  Race. 
D)  Marital status. 
A)  Grade point average. 
B)  Gender. 
C)  Race. 
D)  Marital status.

Question 8

In the first-order model $\hat{y}$ = 60 + 40x1 -10x2 + 5x1x2, a unit increase in x1, while holding x2 constant at 1, increases the value of $y$ on average by 45 units.

Accepted Answer

A) True 
 B)False

Question 9

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 $y =$ $9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$ . $\begin{array}{|c|rrc|}
\hline \text { Predictor } & \text { Coef } & \text { SDev } & \text { T } \
\hline \text { Constant } & 9.14 & 7.10 & 1.287 \
x_{1} & 6.73 & 1.91 & 3.524 \
x_{2} & 10.42 & 4.16 & 2.505 \
x_{3} & 5.16 & 3.93 & 1.313 \
\hline
\end{array}$ S = 15.0 R-Sq = 44.2%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r c c c | } 
\hline \text { Source of Variation } & d f & S S & M S & F \
\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \
\text { Error } & 96 & 21553 & 224.510 & \
\hline \text { Total } & 99 & 38651 & & \
\hline
\end{array}
\end{array}$$ 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

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

Question 10

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 $y =$ $$71.65 + 2.07 x _ { 1 } + 10.16 x _ { 2 } - 7.44 x _ { 3 }$$ . $$\begin{array} { | c | r r c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 71.65 & 18.56 & 3.860 \
x _ { 1 } & 2.07 & 0.81 & 2.556 \
x _ { 2 } & 10.16 & 3.16 & 3.215 \
x _ { 3 } & - 7.44 & 2.85 & - 2.611 \
\hline
\end{array}$$ S = 42.6 R-Sq = 30.9%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & F \
\hline \text { Regression } & 3 & 98008 & 32669.333 & 18.008 \
\text { Error } & 121 & 219508 & 1814.116 & \
\hline \text { Total } & 124 & 317516 & & \
\hline
\end{array}
\end{array}$$ Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the income of professionals?

Accepted Answer

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

Question 11

The owner of an air conditioner business wants to investigate the relationship between the weekly number of air conditioners sold with average weekly temperature and the seasons of the year.
A random sample of 14 weeks is taken, with the average temperature of that week (in degrees Celsius) and the quarter from which that week belonged, noted.
There are three indicator variables: March, September and December.
Excel is used to generate the following multiple linear regression output. \(\begin{array}{|l|r|r|r|r|r|c|}
\hline \text { SUMMARY OUTPUT } & \
\hline \text { Regression Statistics } & \
\hline \text { Multiple R } & 0.99 \
\hline \text { R Square } & 0.97 \
\hline \text { Adjusted RSquare } & 0.96 \
\hline \text { Standard Error } & 4.54 \
\hline \text { Observations } & 14.00 \
\hline\
\hline \text { ANOVA }\
\hline &{\text { df }} &{SS} &MS & F& {\text { Significance }} \
\hline \text { Regression } & 4.00 & 6999.27 & 1749.82 & 84.86 & 0.00 \
\hline \text { Residual } & 9.00 & 185.58 & 20.62 & & \
\hline \text { Total } & 13.00 & 7184.86 & & & \
\hline\
\hline & \text { Coefficients } & \begin{array}{c}
\text { Standard } \
\text { Error }
\end{array} & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}
\text { Upper } \
95 \%
\end{array} \
\hline \text { Intercept } & -17.94 & 8.54 & -2.10 & 0.07 & -37.27 & 1.38 \\hline \text { Temperature } & 1.00 & 0.35 & 2.84 & 0.02 & 0.20 & 1.79 \
\hline \text { March } & 1.01 & 4.60 & 0.22 & 0.83 & -9.39 & 11.40 \
\hline \text { September } & 7.22 & 5.58 & 1.29 & 0.23 & -5.40 & 19.84 \
\hline \text { Deomber } & 27.87 & 6.55 & 4.26 & 0.00 & 13.06 & 42.68 \
\hline
\end{array}\) Test the significance of the coefficient of Temperature, at the 5% level of α. Justify your choice of the alternative hypothesis.

Accepted Answer

Choose to do a right tailed test because

Question 12

Suppose that the sample regression equation of a second-order model is  $= 2.50 + 0.15 x + 0.45 x ^ { 2 }$ . The value 4.60 is the:

Accepted Answer

A)  predicted value of y for any positive value of x. 
B)  predicted value of y when x = 2. 
C)  estimated change in y when x increases by 1 unit. 
D)  intercept where the response surface strikes the x-axis. 
A)  predicted value of y for any positive value of x. 
B)  predicted value of y when x = 2. 
C)  estimated change in y when x increases by 1 unit. 
D)  intercept where the response surface strikes the x-axis.

Question 13

A first-order model was used in a regression analysis involving 25 observations to study the relationship between a dependent variable y and three independent variables, $x _ { 1 }$ , $x _ { 2 }$ and $x _ { 3 }$ . The analysis showed that the mean squares for regression is 160 and the sum of squares for error is 1050. In addition, the following is a partial computer printout. $$\begin{array} { | c | c c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } \
\hline \text { Constant } & 25 & 4 \
x _ { 1 } & 18 & 6 \
x _ { 2 } & - 12 & 4.8 \
x _ { 3 } & 6 & 5 \
\hline
\end{array}$$ Is there sufficient evidence at the 5% significance level to indicate that $x _ { 3 }$ is positively linearly related to y?

Accepted Answer

@#IMG-DLM& . @#IMG-DLM& .
Rejection regi

Question 14

The model y = $\beta$0 + $\beta$1x + $\varepsilon$ is referred to as a simple linear regression model.

Accepted Answer

A) True 
 B)False

Question 15

A first-order model was used in a regression analysis involving 25 observations to study the relationship between a dependent variable y and three independent variables, $x _ { 1 }$ , $x _ { 2 }$ and $x _ { 3 }$ . The analysis showed that the mean squares for regression is 160 and the sum of squares for error is 1050. In addition, the following is a partial computer printout. $$\begin{array} { | c | c c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } \
\hline \text { Constant } & 25 & 4 \
x _ { 1 } & 18 & 6 \
x _ { 2 } & - 12 & 4.8 \
x _ { 3 } & 6 & 5 \
\hline
\end{array}$$ Is there enough evidence at the 5% significance level to conclude that the model is useful in predicting the value of y?

Accepted Answer

@#IMG-DLM& . @#IMG-DLM& At least one @#IMG-DLM& .
Rejection

Question 16

In explaining students' test scores, which of the following independent variables would not be adequately represented by an indicator variable?

Accepted Answer

A)  Gender 
B)  Cultural background 
C)  Number of hours studying for the test 
D)  Marital status 
A)  Gender 
B)  Cultural background 
C)  Number of hours studying for the test 
D)  Marital status

Question 17

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 simple linear model?

Accepted Answer

@#IMG-DLM& 0.589, which means that about 59% of th

Question 18

Suppose that the sample regression equation of a model is  $=4.7+2.2 x_{1}+2.6 x_{2}-x_{1} x_{2}$ . If we examine the relationship between y and $x _ { 2 }$ for $x _ { 1 }$ = 1, 2 and 3, we observe that the three equations produced not only differ in the intercept term, but the coefficient of $x _ { 2 }$ also varies.

Accepted Answer

A) True 
 B)False

Question 19

Regression analysis allows the statistics practitioner to use mathematical models to realistically describe relationships between the dependent variable and independent variables.

Accepted Answer

A) True 
 B)False

Question 20

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 $y =$ $71.65 + 2.07 x _ { 1 } + 10.16 x _ { 2 } - 7.44 x _ { 3 }$ . $$\begin{array} { | c | r r c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 71.65 & 18.56 & 3.860 \
x _ { 1 } & 2.07 & 0.81 & 2.556 \
x _ { 2 } & 10.16 & 3.16 & 3.215 \
x _ { 3 } & - 7.44 & 2.85 & - 2.611 \
\hline
\end{array}$$ S = 42.6 R-Sq = 30.9%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | r c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & F \
\hline \text { Regression } & 3 & 98008 & 32669.333 & 18.008 \
\text { Error } & 121 & 219508 & 1814.116 & \
\hline \text { Total } & 124 & 317516 & & \
\hline
\end{array}
\end{array}$$ Is there enough evidence at the1% significant level to conclude that physicians earn more on average than lawyers?

Accepted Answer

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

In general, to represent a nominal independent variable that has n possible categories, we would create n dummy variables.

The model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ + $\varepsilon$ is referred to as a:

A regression analysis involving 40 observations and five independent variables revealed that the total variation in the dependent variable y is 1080 and that the mean square for error is 30. Create the ANOVA table.

In explaining starting salaries for graduates of computer science programs, which of the following independent variables would not be adequately represented with a dummy variable?

In the first-order model $\hat{y}$ = 60 + 40x₁ -10x₂ + 5x₁x₂, a unit increase in x₁, while holding x₂ constant at 1, increases the value of $y$ on average by 45 units.

Suppose that the sample regression equation of a second-order model is $Suppose that the sample regression equation of a second-order model is = 2.50 + 0.15 x + 0.45 x ^ { 2 } . The value 4.60 is the:$ $= 2.50 + 0.15 x + 0.45 x ^ { 2 }$ . The value 4.60 is the:

The model y = $\beta$ ₀ + $\beta$ ₁x + $\varepsilon$ is referred to as a simple linear regression model.

In explaining students' test scores, which of the following independent variables would not be adequately represented by an indicator variable?

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 simple linear model?

Regression analysis allows the statistics practitioner to use mathematical models to realistically describe relationships between the dependent variable and independent variables.

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 general, to represent a nominal independent variable that has n possible categories, we would create n dummy variables.

The model y=β0+β1x1+β2x2+β3x1x2y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }y=β0​+β1​x1​+β2​x2​+β3​x1​x2​ + ε\varepsilonε is referred to as a:

A regression analysis involving 40 observations and five independent variables revealed that the total variation in the dependent variable y is 1080 and that the mean square for error is 30. Create the ANOVA table.

In explaining starting salaries for graduates of computer science programs, which of the following independent variables would not be adequately represented with a dummy variable?

In the first-order model y^\hat{y}y^​ = 60 + 40x1 -10x2 + 5x1x2, a unit increase in x1, while holding x2 constant at 1, increases the value of yyy on average by 45 units.

Suppose that the sample regression equation of a second-order model is =2.50+0.15x+0.45x2= 2.50 + 0.15 x + 0.45 x ^ { 2 }=2.50+0.15x+0.45x2 . The value 4.60 is the:

The model y = β\betaβ 0 + β\betaβ 1x + ε\varepsilonε is referred to as a simple linear regression model.

In explaining students' test scores, which of the following independent variables would not be adequately represented by an indicator variable?

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 simple linear model?

Regression analysis allows the statistics practitioner to use mathematical models to realistically describe relationships between the dependent variable and independent variables.

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

The model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ + $\varepsilon$ is referred to as a:

In the first-order model $\hat{y}$ = 60 + 40x₁ -10x₂ + 5x₁x₂, a unit increase in x₁, while holding x₂ constant at 1, increases the value of $y$ on average by 45 units.

Suppose that the sample regression equation of a second-order model is $Suppose that the sample regression equation of a second-order model is = 2.50 + 0.15 x + 0.45 x ^ { 2 } . The value 4.60 is the:$ $= 2.50 + 0.15 x + 0.45 x ^ { 2 }$ . The value 4.60 is the:

The model y = $\beta$ ₀ + $\beta$ ₁x + $\varepsilon$ is referred to as a simple linear regression model.