Deck 9: Regression Analysis

Question 1

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

The R² value:

A)is the variability of the observed Y-values from the predicted values.
B)indicates that as the independent variable increases, the intercept term does too.
C)gives the proportion of variation in the dependent variable that is explained by the independent variable.
D)transforms the cumulative probability scale (vertical axis)so that the graph of the cumulative normal distribution is a straight line.

Answer 1

C

Question 2

Regression models of ________ data focus on predicting the future.

A)missing
B)time-series
C)panel
D)cross-sectional

Answer 2

B

Question 3

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

Which of the following Excel functions is applied to test for significance of regression?

A)COVAR
B)ANOVA
C)SINH
D)TREND

Answer 3

B

Question 4

A regression model that involves a single independent variable is called ________.

A)single regression
B)unit regression
C)simple regression
D)individual regression

Question 5

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

What is the value of the coefficient b₁?

A)86.81704
B)254.8371
C)0)010697
D)-2.14625

Question 6

________ provide information about the unknown values of the true regression coefficients, accounting for sampling error.

A)Standard errors
B)Confidence intervals
C)Adjusted R Squares
D)P-values

Question 7

The following table exhibits the age of antique furniture and the corresponding prices.Use the table to answer the following question(s).(Hint: Use scatter diagram and the Excel Trendline tool where necessary).

Which of the following equations correctly expresses the relationship between the two variables?

A)Value = (-181.16)+ 13.493 × Number of years
B)Number of years = Value / 12.537
C)Value = (459.34 / Number of years)× 4.536
D)Number of years = (17.538 × Value)/ (-157.49)

Question 8

The following table exhibits the age of antique furniture and the corresponding prices.Use the table to answer the following question(s).(Hint: Use scatter diagram and the Excel Trendline tool where necessary).

In a linear relationship, which of the following accounts for the many possible values of the dependent variable that vary around the mean?

A)the coefficient of the dependent variable X
B)the value of the intercept ß₀
C)the random error term ε
D)the standard error SYX

Question 9

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

For a simple linear regression model, significance of regression is:

A)a measure of how well the regression line fits the data.
B)a hypothesis test of whether the regression coefficient ß1 is zero.
C)a statistic that modifies the value of R² by incorporating the sample size and the number of explanatory variables in the model.
D)the variability of the observed Y-values from the predicted values.

Question 10

The following table exhibits the age of antique furniture and the corresponding prices.Use the table to answer the following question(s).(Hint: Use scatter diagram and the Excel Trendline tool where necessary).

Which of the following is true about the observed errors associated with estimating the value of the dependent variable using the regression line?

A)They are the horizontal distances between slopes and y-intercepts.
B)The errors are also referred to as critical values.
C)They are always maximized by the regression lines.
D)The errors can be negative or positive.

Question 11

The following table exhibits the age of antique furniture and the corresponding prices.Use the table to answer the following question(s).(Hint: Use scatter diagram and the Excel Trendline tool where necessary).

What is the expected value for a 90 year-old piece of furniture?

A)$1002.45
B)$997.98
C)$934.56
D)$1033.21

Question 12

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

What is the value of the coefficient b₀?

A)-2.25321
B)0)010697
C)254.8371
D)86.81704

Question 13

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

What is the estimated cost of raising a 10-inch wall?

A)1505.786
B)1103.578
C)968.6109
D)1123.008

Question 14

The following table exhibits the age of antique furniture and the corresponding prices.Use the table to answer the following question(s).(Hint: Use scatter diagram and the Excel Trendline tool where necessary).

What is the relationship between the age of the furniture and their values?

A)Nonlinear
B)Linear
C)Curvilinear
D)No relationship

Question 15

Standard residuals:

A)help detect outliers that may bias the results of a regression analysis.
B)cause differences in the regression equation by changing the slope and intercept.
C)point out the ranges for the population intercept and slope at a 95% confidence level.
D)provide information for testing hypothesis associated with the intercept and slope.

Question 16

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

Which of the following is true about Excel outputs Multiple R?

A)It is often referred to as the coefficient of determination.
B)A value of 0 indicates positive correlation.
C)A negative slope of the regression line denotes a positive Multiple R.
D)It is another name for the sample correlation coefficient, r.

Question 17

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

While testing hypotheses for regression coefficients, the t-test for the slope is expressed as:

A)t =
B)t =
C)t =
D)t =

Question 18

The following table exhibits the age of antique furniture and the corresponding prices.Use the table to answer the following question(s).(Hint: Use scatter diagram and the Excel Trendline tool where necessary).

For an independent variable Y, the error associated with the iᵗʰ observation is:

A)eᵢ = Yᵢ - Ŷᵢ
B)Yᵢ = (eᵢ)² - Ŷᵢ
C) (Ŷᵢ)² ᵉᵢ = Yᵢ
D)eᵢ = (Yᵢ + Ŷᵢ)²

Question 19

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

Which of the following statements is true when using the Excel Regression tool?

A)The range for the independent variable values must be specified in the box for the Input Y Range.
B)Checking the option Constant is Zero forces the intercept to zero.
C)The Regression tool can be found in the Tools tab under Insert group.
D)Adding an intercept term reduces the analysis' fit to the data.

Question 20

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).

Which of the following generates a scatter chart in Excel with the values predicted by the regression model included?

A)Trendline
B)Residual Plots
C)R Square
D)Line Fit Plots

Question 21

How many additional dummy variables are required if a categorical variable has 4 levels?

A)2
B)3
C)1
D)4

Question 22

Which of the following helps in evaluation of autocorrelation?

A)Breusch-Pagan test
B)Durbin-Watson statistic
C)Hosmer-Lemeshow test
D)Cochran-Mantel-Haenszel statistics

Question 23

A(n)________ is an extreme value that is different from the rest of the data.

A)critical value
B)standard error
C)expected value
D)outlier

Question 24

Categorical variables that have been coded are called ________.

A)limited dependent variables
B)dummy variables
C)instrumental variables
D)observable variables

Question 25

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Draw conclusions for test of hypothesis for regression coefficients.

Question 26

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Is the hours spent on the job a statistically significant variable in explaining the variation in pay of employees? (Hint: Use Regression tool).

Question 27

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Interpret residual output.

Question 28

________ means that the variation about the regression line is constant for all values of the independent variable.

A)Autocorrelation
B)Normality of errors
C)Homoscedasticity
D)Linearity

Question 29

Which of the following is true when testing for normality of errors?

A)Normality is verified by inspecting for a bell-shaped distribution.
B)It is easier to evaluate normality with small sample sizes.
C)A scatter diagram of the whole data is always used to verify normality.
D)Errors are normally distributed when the scatter diagram shows a straight-line distribution.

Question 30

In a curvilinear regression model, the ________ represents the curvilinear effect.

A)intercept
B)error term
C)slope
D)R Square

Question 31

Which of the following is true about multiple linear regression?

A)It is a linear regression model with more than one dependent variable.
B)The regression coefficients are called fractional regression coefficients.
C)It uses least squares to estimate the intercept and slope coefficients.
D)The ANOVA tests for the significance of each variable separately.

Question 32

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Interpret the confidence intervals.

Question 33

Which of the following is true about multicollinearity?

A)The effect of a dependent variable on another becomes difficult to isolate.
B)Regression coefficients become clearer and are easier to interpret.
C)P-values reduce significantly leading to rejection of null hypothesis.
D)It is best measured using the statistic variance inflation factor (VIF).

Question 34

When using the t-statistic in multiple regression to determine if a variable should be removed:

A)R² will increase if the variable is removed.
B)if |t| > 1, the standard error will decrease.
C)a large number of independent variables is convenient.
D)if |t| < 1, the standard error will increase.

Question 35

While checking for linearity by examining the residual plot, the residuals must:

A)exhibit a linear trend.
B)form a parabolic shape.
C)be randomly scattered.
D)be below the x-axis.

Question 36

When a scatter chart of data shows a nonlinear relationship, the nonlinear model can be expressed as:

A)Y = β₀ ⁺ β₁X + β₂X² + ε
B)Y = β₀ ⁺ β₁X + (β₂X)² + ε
C)Y = β₀ ⁺ β₁X + β₂X
D)Y = β₀ ⁺ β₁X² + β₂X² + ε

Question 37

Interaction is:

A)the principle of having a model with maximum explanatory variables.
B)the process of coding categorical variables.
C)a measure to determine the correlation between dependent variables.
D)the dependence between two independent variables.

Question 38

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Construct a scatter diagram and use the Excel Trendline tool to find the best-fitting simple linear regression model.

Question 39

In multiple regression, R Square is referred to as the:

A)multiple correlation coefficient.
B)coefficient of autocorrelation.
C)coefficient of multiple determination.
D)multiple significance coefficient.

Question 40

When two or more independent variables in the same regression model can predict each other better than the dependent variable, the condition is referred to as ________.

A)autocorrelation
B)heteroscedasticity
C)multicollinearity
D)homoscedasticity

Question 41

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

The best-fitting line maximizes the residuals.

Question 42

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

A good regression model has the fewest number of explanatory variables providing an adequate interpretation of the dependent variable.

Question 43

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Briefly explain the assumptions on which the statistical hypothesis tests associated with regression analysis are predicated.

Question 44

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

The standard error may be assumed to be large if the data are clustered close to the regression line.

Question 45

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Creating a scatter chart with an added trendline is visually superior to the scatter chart generated by line fit plots.

Question 46

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Why is regression analysis necessary in business? What categories of regression models are used?

Question 47

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

List the systematic approach to building good multiple regression models.

Question 48

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

Explain the concept of curvilinear regression model.

Question 49

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

An increase in adjusted R² indicates that the regression model has improved.

Question 50

Use the data given below to answer the following question(s).
Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay.(Note: Assume a level of significance of 0.05 wherever necessary.)

While conducting regression analysis, how is constructing a normal probability plot useful?