Deck 8: Trendlines and Regression Analysis

Question 1

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

Answer 1

A

Question 2

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)

Answer 2

A

Question 3

Identify the components of simple linear regression models and discuss their applications 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 ? = b0 + b1X. (Hint: Use Excel functions). $$\begin{array} { | l | l | } \hline\begin{array} { l } \text { Height } \\\text { (ft) }\end{array} & \text { Cost (\$) } \\\hline 4 & 670 \\\hline 3 & 430 \\\hline 7 & 810 \\\hline 9 & 1100 \\\hline 6 & 790 \\\hline 8 & 880 \\\hline 5 & 760 \\\hline 11 & 1200 \\\hline\end{array}$$

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

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

Answer 3

1123.008

Question 4

Regression models of data focus on predicting the future.

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

Question 5

Identify the components of simple linear regression models and discuss their applications 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 ? = b0 + b1X. (Hint: Use Excel functions). $$\begin{array} { | l | l | } \hline\begin{array} { l } \text { Height } \\\text { (ft) }\end{array} & \text { Cost (\$) } \\\hline 4 & 670 \\\hline 3 & 430 \\\hline 7 & 810 \\\hline 9 & 1100 \\\hline 6 & 790 \\\hline 8 & 880 \\\hline 5 & 760 \\\hline 11 & 1200 \\\hline\end{array}$$

-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 6

Which of the following is true of the R-squared (R2) value in Excel's Trendline function?

A) A value of 1.0 for R2 indicates maximum deviation of the data from the line.
B) If the value of R2 is above 1.0, the line will be at a perfect fit for the data.
C) The value of R2 will always be between -1 and 1.
D) As the value of R2 gets higher, the line will be a better fit for the data.

Question 7

Identify the components of simple linear regression models and discuss their applications 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 ? = b0 + b1X. (Hint: Use Excel functions). $$\begin{array} { | l | l | } \hline\begin{array} { l } \text { Height } \\\text { (ft) }\end{array} & \text { Cost (\$) } \\\hline 4 & 670 \\\hline 3 & 430 \\\hline 7 & 810 \\\hline 9 & 1100 \\\hline 6 & 790 \\\hline 8 & 880 \\\hline 5 & 760 \\\hline 11 & 1200 \\\hline\end{array}$$

-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 8

Identify the components of simple linear regression models and discuss their applications 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 ? = b0 + b1X. (Hint: Use Excel functions). $$\begin{array} { | l | l | } \hline\begin{array} { l } \text { Height } \\\text { (ft) }\end{array} & \text { Cost (\$) } \\\hline 4 & 670 \\\hline 3 & 430 \\\hline 7 & 810 \\\hline 9 & 1100 \\\hline 6 & 790 \\\hline 8 & 880 \\\hline 5 & 760 \\\hline 11 & 1200 \\\hline\end{array}$$

-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 9

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.

Question 10

In functions, represented by y = abx, y rises or falls at constantly increasing rates.

A) logarithmic
B) power
C) exponential
D) polynomial

Question 11

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

Identify the components of simple linear regression models and discuss their applications
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). $$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Number } \\\text { of years }\end{array} & \begin{array} { l } \text { Value } \\\text { (\$) }\end{array} \\\hline 78 & 930 \\\hline 91 & 1010 \\\hline 83 & 970 \\\hline 159 & 1950 \\\hline 134 & 1610 \\\hline 210 & 2880 \\\hline 88 & 980 \\\hline 178 & 2010 \\\hline 124 & 1370 \\\hline 72 & 900 \\\hline\end{array}$$

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

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

Question 13

Identify the components of simple linear regression models and discuss their applications 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 ? = b0 + b1X. (Hint: Use Excel functions). $$\begin{array} { | l | l | } \hline\begin{array} { l } \text { Height } \\\text { (ft) }\end{array} & \text { Cost (\$) } \\\hline 4 & 670 \\\hline 3 & 430 \\\hline 7 & 810 \\\hline 9 & 1100 \\\hline 6 & 790 \\\hline 8 & 880 \\\hline 5 & 760 \\\hline 11 & 1200 \\\hline\end{array}$$

-What is the value of the coefficient b1?

A) 86.81704
B) 254.8371
C) 0.010697
D) -2.14625

Question 14

Identify the components of simple linear regression models and discuss their applications
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). $$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Number } \\\text { of years }\end{array} & \begin{array} { l } \text { Value } \\\text { (\$) }\end{array} \\\hline 78 & 930 \\\hline 91 & 1010 \\\hline 83 & 970 \\\hline 159 & 1950 \\\hline 134 & 1610 \\\hline 210 & 2880 \\\hline 88 & 980 \\\hline 178 & 2010 \\\hline 124 & 1370 \\\hline 72 & 900 \\\hline\end{array}$$

-Which of the following is true of linear functions used in predictive analytical models?

A) It is used when the rate of change in a variable decreases or increases quickly and then levels out.
B) It is used when there is a steady decrease or increase over a range of a variable.
C) It is used when there is increase at a specific rate.
D) It is used when there is a rise or fall at a constantly increasing rate.

Question 15

Identify the components of simple linear regression models and discuss their applications 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 ? = b0 + b1X. (Hint: Use Excel functions). $$\begin{array} { | l | l | } \hline\begin{array} { l } \text { Height } \\\text { (ft) }\end{array} & \text { Cost (\$) } \\\hline 4 & 670 \\\hline 3 & 430 \\\hline 7 & 810 \\\hline 9 & 1100 \\\hline 6 & 790 \\\hline 8 & 880 \\\hline 5 & 760 \\\hline 11 & 1200 \\\hline\end{array}$$

-What is the value of the coefficient b0?

A) -2.25321
B) 0.010697
C) 254.8371
D) 86.81704

Question 16

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 17

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

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

Question 18

In Excel's Trendline tool, the value of the gives the measure of fit of the line to the data.

A) linear function
B) R-squared
C) moving average
D) set intercept

Question 19

Which of the following mathematical functions, used in predictive analytical models, is represented by the formula y = ax3 + bx2 + cx + d?

A) exponential functions
B) power functions
C) logarithmic functions
D) polynomial functions

Question 20

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 21

Categorical variables that have been coded are called .

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

Question 22

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 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

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 25

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 26

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 27

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 28

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 29

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

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

Question 30

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

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

Question 31

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

Question 32

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 33

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 34

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 true 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 35

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

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

Question 36

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 37

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 38

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 39

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 40

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 41

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

Question 42

List the systematic approach to build good multiple regression models.

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

Question 44

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

Question 45

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

Question 46

Explain the concept of curvilinear regression model.

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.)
Draw conclusions for test of hypothesis for regression coefficients.

Question 48

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

Question 49

The best-fitting line maximizes the residuals.

Question 50

Interpret residual output.

Question 51

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 52

Excel's Trendline feature cannot be used in modeling trends which include time variables.

Question 53

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

Question 54

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

Question 55

Interpret the confidence intervals.

Question 56

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

Question 57

When are logarithmic functions used in predictive analysis?

Question 58

In predictive analysis models, a second-order polynomial has only one hill or valley.