An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $X _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS $y=1.74+0.091 x_{1}+0.93 x_{2}+0.26 x_{3}$ $\begin{array}{|c|ccc|} \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm{T} \\ \hline \text { Constant } & 1.74 & 0.630 & 2.762 \\ x_{1} & 0.091 & 0.025 & 3.640 \\ x_{2} & 0.93 & 0.290 & 3.207 \\ x_{3} & 0.26 & 0.180 & 1.444 \\ \hline \end{array}$ \[\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%\] ANALYSIS OF VARIANCE $\begin{array}{|l|cccc|} \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 288 & 96 & 22.647 \\ \text { Error } & 46 & 195 & 4.239 & \\ \hline \text { Total } & 49 & 483 & & \\ \hline \end{array}$ Test at the 10% significance level to determine whether annual household income and annual family clothes expenditure are linearly related.

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

A multiple regression model has the form ŷ = b0 + b1x1 + b2x2. Which of the following best describes b2?

A) We estimate for each one unit increase in x2, that y will increase by b2 units, on average. B) Whilst holding x1 constant, we estimate for each one unit increase in x2, that y will increase by b2 units, on average. C) Whilst holding x2 constant, we estimate for each one unit increase in x1, that y will increase by b2 units, on average. D) Whilst holding x1 constant, we estimate for each one unit increase in x2, that y will increase by b1 units, on average. A) We estimate for each one unit increase in x2, that y will increase by b2 units, on average. B) Whilst holding x1 constant, we estimate for each one unit increase in x2, that y will increase by b2 units, on average. C) Whilst holding x2 constant, we estimate for each one unit increase in x1, that y will increase by b2 units, on average. D) Whilst holding x1 constant, we estimate for each one unit increase in x2, that y will increase by b1 units, on average.

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $x _ { 1 }$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $X _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below: THE REGRESSION EQUATION IS $y =$ \[55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }\] \[\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \\ \hline \text { Constant } & 55.8 & 11.8 & 4.729 \\ x _ { 1 } & 1.79 & 0.44 & 4.068 \\ x _ { 2 } & - 0.021 & 0.011 & - 1.909 \\ x _ { 3 } & - 0.016 & 0.014 & - 1.143 \\ \hline \end{array}\] S = 9.47 R-Sq = 22.5%. \[\begin{array}{l} \text { ANALYSIS OF VARIANCE }\\ \begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 936 & 312 & 3.477 \\ \text { Error } & 36 & 3230 & 89.722 & \\ \hline \text { Total } & 39 & 4166 & & \\ \hline \end{array} \end{array}\] Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?

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

An estimated multiple regression model has the form ŷ = 100 − 2x1 + 9x2. As x1 increases by 1 unit while holding x2 constant, which of the following best describes the change in y?

A) y will increase by 2 units, estimated, on average. B) y will decrease by 98 units, estimated, on average. C) y will increase by 98 units, estimated, on average. D) y will decrease by 2 units, estimated, on average. A) y will increase by 2 units, estimated, on average. B) y will decrease by 98 units, estimated, on average. C) y will increase by 98 units, estimated, on average. D) y will decrease by 2 units, estimated, on average.

A statistician wanted to determine whether the demographic variables of age, education and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = number of hours of television watched last week. $x _ { 1 }$ = age. $x _ { 2 }$ = number of years of education. $X _ { 3 }$ = income (in $1000s). The computer output is shown below. THE REGRESSION EQUATION IS $y =$ \[22.3 + 0.41 x _ { 1 } - 0.29 x _ { 2 } - 0.12 x _ { 3 }\] \[\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\ \hline \text { Constant } & 22.3 & 10.7 & 2.084 \\ x _ { 1 } & 0.41 & 0.19 & 2.158 \\ x _ { 2 } & - 0.29 & 0.13 & - 2.231 \\ x _ { 3 } & - 0.12 & 0.03 & - 4.00 \\ \hline \end{array}\] S = 4.51 R-Sq = 34.8%. \[\begin{array}{l} \text { ANALYSIS OF VARIANCE }\\ \begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 227 & 75.667 & 3.730 \\ \text { Error } & 21 & 426 & 20.286 & \\ \hline \text { Total } & 24 & 653 & & \\ \hline \end{array} \end{array}\] Is there sufficient evidence at the 1% significance level to indicate that hours of television watched and age are linearly related?

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

Exam 19: Multiple Regression

Given the multiple linear regression equation $Given the multiple linear regression equation = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 } , the value -0.80 is the y intercept.$ $= - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the $y$ intercept.

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Question 61

A statistician wanted to determine whether the demographic variables of age, education and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = number of hours of television watched last week. $x _ { 1 }$ = age. $x _ { 2 }$ = number of years of education. $X _ { 3 }$ = income (in $1000s). The computer output is shown below. THE REGRESSION EQUATION IS $y =$ $22.3 + 0.41 x _ { 1 } - 0.29 x _ { 2 } - 0.12 x _ { 3 }$ Predictor Coef StDev Constant 22.3 10.7 2.084 0.41 0.19 2.158 -0.29 0.13 -2.231 -0.12 0.03 -4.00 S = 4.51 R-Sq = 34.8%. ANALYSIS OF VARIANCE Source of Variation df SS MS F Regression 3 227 75.667 3.730 Error 21 426 20.286 Total 24 653 Interpret the coefficient $b _ { 2 }$ .

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Question 62

Given the multiple linear regression equation, ŷ = b₀+ b₁x₁ + b₂x₂, the value of b₂ is the estimated average increase in y for a one unit increase in x₂, whilst holding x₁ constant.

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Question 63

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) and number of different pastries and biscuits offered to customers 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 and number of different pastries and biscuits offered on that day, noted. Describe the following scatterplots. Scatterplot of Daily hot coffee sales revenue vs Temperature Scatterplot of Daily hot coffee sales revenue Pastries/biscuits Residual scatterplot of Daily hot coffee sales revenue vs fitted values

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Question 64

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A Pop-up coffee vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers, 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 and number of different pastries and biscuits offered on that day, noted. Excel output for a multiple linear regression is given below: Coffee sales revenue Temperature Pastries/biscuits 6.5 25 7 10 17 13 5.5 30 5 4.5 35 6 3.5 40 3 28 9 15 $Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A Pop-up coffee vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers, impacts daily hot coffee sales revenue (in $00's). A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted. Excel output for a multiple linear regression is given below: \begin{array} { | c | c | r | } \hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \\ \hline 6.5 & 25 & 7 \\ \hline 10 & 17 & 13 \\ \hline 5.5 & 30 & 5 \\ \hline 4.5 & 35 & 6 \\ \hline 3.5 & 40 & 3 \\ \hline 28 & 9 & 15 \\ \hline \end{array} a. Write down the multiple regression model. b. Interpret the coefficient of Temperature. c. Interpret the coefficient of Pastries/biscuits.$ a. Write down the multiple regression model. b. Interpret the coefficient of Temperature. c. Interpret the coefficient of Pastries/biscuits.

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Question 65

If multicollinearity exists among the independent variables included in a multiple regression model, then:

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Question 66

In a multiple regression model, the mean of the probability distribution of the error variable $\varepsilon$ is assumed to be:

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Question 67

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $X _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS $y=1.74+0.091 x_{1}+0.93 x_{2}+0.26 x_{3}$ Predictor Coef StDev Constant 1.74 0.630 2.762 0.091 0.025 3.640 0.93 0.290 3.207 0.26 0.180 1.444 $\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$ ANALYSIS OF VARIANCE Source of Variation df SS MS F Regression 3 288 96 22.647 Error 46 195 4.239 Total 49 483 Test at the 10% significance level to determine whether annual household income and annual family clothes expenditure are linearly related.

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Question 68

A multiple regression model has the form ŷ = b₀+ b₁x₁ + b₂x₂. Which of the following best describes b₂?

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Question 69

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations, the number of degrees of freedom for the numerator and denominator for the critical value of F are 4 and 26, respectively.

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Question 70

Multiple linear regression is used to estimate the linear relationship between one dependent variable and more than one independent variables.

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Question 71

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

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Question 72

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $x _ { 1 }$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $X _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below: THE REGRESSION EQUATION IS $y =$ $55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$ Predictor Coef StDev T Constant 55.8 11.8 4.729 1.79 0.44 4.068 -0.021 0.011 -1.909 -0.016 0.014 -1.143 S = 9.47 R-Sq = 22.5%. ANALYSIS OF VARIANCE Source of Variation df SS MS F Regression 3 936 312 3.477 Error 36 3230 89.722 Total 39 4166 Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?

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Question 73

The computer output for the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \xi$ is shown below. However, because of a printer malfunction some of the results are not shown. These are indicated by the boldface letters a to i. Fill in the missing results (up to three decimal places). Predictor Coef StDev Constant a 0.120 3.18 0.068 b 3.38 0.024 0.010 c S = d R-Sq = e. ANALYSIS OF VARIANCE Source of Variation df SS MS F Regression 2 7.382 g i Error 22 f h Total 24 7.530

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Question 74

An estimated multiple regression model has the form ŷ = 100 − 2x₁+ 9x₂. As x₁ increases by 1 unit while holding x₂ constant, which of the following best describes the change in y?

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Question 75

A statistician wanted to determine whether the demographic variables of age, education and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = number of hours of television watched last week. $x _ { 1 }$ = age. $x _ { 2 }$ = number of years of education. $X _ { 3 }$ = income (in $1000s). The computer output is shown below. THE REGRESSION EQUATION IS $y =$ $22.3 + 0.41 x _ { 1 } - 0.29 x _ { 2 } - 0.12 x _ { 3 }$ Predictor Coef StDev Constant 22.3 10.7 2.084 0.41 0.19 2.158 -0.29 0.13 -2.231 -0.12 0.03 -4.00 S = 4.51 R-Sq = 34.8%. ANALYSIS OF VARIANCE Source of Variation df SS MS F Regression 3 227 75.667 3.730 Error 21 426 20.286 Total 24 653 Is there sufficient evidence at the 1% significance level to indicate that hours of television watched and age are linearly related?

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Question 76

A multiple regression model has the form ŷ = 24- 0.001x₁ + 3x₂. As x₁ increases by 1 unit, holding $x _ { 2 }$ constant, the value of y is estimated to decrease by 0.001units, on average.

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Question 77

Which of the following measures can be used to assess a multiple regression model's fit?

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Question 78

In multiple regression, and because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

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Question 79

Which of the following best describes the range of the coefficient of multiple determination?

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Question 80

Showing 61 - 80 of 121

Given the multiple linear regression equation $Given the multiple linear regression equation = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 } , the value -0.80 is the y intercept.$ $= - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the $y$ intercept.

Given the multiple linear regression equation, ŷ = b₀+ b₁x₁ + b₂x₂, the value of b₂ is the estimated average increase in y for a one unit increase in x₂, whilst holding x₁ constant.

If multicollinearity exists among the independent variables included in a multiple regression model, then:

In a multiple regression model, the mean of the probability distribution of the error variable $\varepsilon$ is assumed to be:

A multiple regression model has the form ŷ = b₀+ b₁x₁ + b₂x₂. Which of the following best describes b₂?

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations, the number of degrees of freedom for the numerator and denominator for the critical value of F are 4 and 26, respectively.

Multiple linear regression is used to estimate the linear relationship between one dependent variable and more than one independent variables.

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

An estimated multiple regression model has the form ŷ = 100 − 2x₁+ 9x₂. As x₁ increases by 1 unit while holding x₂ constant, which of the following best describes the change in y?

A multiple regression model has the form ŷ = 24- 0.001x₁ + 3x₂. As x₁ increases by 1 unit, holding $x _ { 2 }$ constant, the value of y is estimated to decrease by 0.001units, on average.

Which of the following measures can be used to assess a multiple regression model's fit?

In multiple regression, and because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

Which of the following best describes the range of the coefficient of multiple determination?

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

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 19: Multiple Regression

Given the multiple linear regression equation =−0.80+0.12x1+0.08x2= - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }=−0.80+0.12x1​+0.08x2​ , the value -0.80 is the yyy intercept.

Given the multiple linear regression equation, ŷ = b0 + b1x1 + b2x2, the value of b2 is the estimated average increase in y for a one unit increase in x2, whilst holding x1 constant.

If multicollinearity exists among the independent variables included in a multiple regression model, then:

In a multiple regression model, the mean of the probability distribution of the error variable ε\varepsilonε is assumed to be:

A multiple regression model has the form ŷ = b0 + b1x1 + b2x2. Which of the following best describes b2?

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations, the number of degrees of freedom for the numerator and denominator for the critical value of F are 4 and 26, respectively.

Multiple linear regression is used to estimate the linear relationship between one dependent variable and more than one independent variables.

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

An estimated multiple regression model has the form ŷ = 100 − 2x1 + 9x2. As x1 increases by 1 unit while holding x2 constant, which of the following best describes the change in y?

A multiple regression model has the form ŷ = 24 - 0.001x1 + 3x2. As x1 increases by 1 unit, holding x2x _ { 2 }x2​ constant, the value of y is estimated to decrease by 0.001units, on average.

Which of the following measures can be used to assess a multiple regression model's fit?

In multiple regression, and because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

Which of the following best describes the range of the coefficient of multiple determination?

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

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Given the multiple linear regression equation $Given the multiple linear regression equation = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 } , the value -0.80 is the y intercept.$ $= - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the $y$ intercept.

Given the multiple linear regression equation, ŷ = b₀+ b₁x₁ + b₂x₂, the value of b₂ is the estimated average increase in y for a one unit increase in x₂, whilst holding x₁ constant.

In a multiple regression model, the mean of the probability distribution of the error variable $\varepsilon$ is assumed to be:

A multiple regression model has the form ŷ = b₀+ b₁x₁ + b₂x₂. Which of the following best describes b₂?

An estimated multiple regression model has the form ŷ = 100 − 2x₁+ 9x₂. As x₁ increases by 1 unit while holding x₂ constant, which of the following best describes the change in y?

A multiple regression model has the form ŷ = 24- 0.001x₁ + 3x₂. As x₁ increases by 1 unit, holding $x _ { 2 }$ constant, the value of y is estimated to decrease by 0.001units, on average.