QBA 3305 Exam #2 Turner

Why is forecasting being considered essential to managing a firm? a.) To develop plans for possible new plants. b.) To have raw materials available for future demand. c.) To develop plans for future financing. d.) To have enough staff for future needs.

All of the above

Components of Time Series

1.) Secular Trend 2.) Cyclical Variation 3.) Seasonal Variation 4.) Irregular Variation (Episodic and Residual)

Assumptions of Residuals

1.) The mean of the residuals = 0 2.) There are no severe outliers. 3.) The residuals are normally distributed. 4.) The residuals display homoscedasticity.

Two Requirements for Good Predictor (Logistic Regression)

1.) The p-value must be less than alpha 2.) BIC must be positive

Why is it important to check the correlation matrix?

It is important to check to ensure that there are not any x variables correlated with each other. (Multicollinearity)

Cyclical Variation

Leads to the values rising and falling over a period of usually more than one year. Often linked to the business cycle, where a period of prosperity will tend to inflate various economic measures, such as sales, and an economic recession will tend to lessen business activity and dampen various time series.

Random Determination (Logistic Regression)

Look at the confusion matrix, add across the row which is the denominator. Number predicted correctly on that row is the numerator. If ratios are "close" than they are random.

Is B0, the y-intercept a variable?

No, it simply depicts where the line crosses the y axis.

R Square in Logistic Regression

Does not usually yield an R square as high as multiple regression models for continuous variables. R square merely describes how useful the model is at predicting the dependent (nominal) variable.

Irregular Variation (Episodic)

Due to unpredictable, random events. Episodic events are defined as things that can be identified after the fact, but not predicted.

Multicollinearity

Happens when two x variables have a strong correlation in the correlation matrix, throwing off the predictive model.

An analysis of past season fluctuations can be helpful in planning production for items such as: toys, greeting cards, decorations, and other holiday-oriented goods, for determining the number of employees needed (part-time help), inventory fluctuations based on time of year, and for determining funding needed. True or False?

True

t corresponds to what in this chapter?

Time

The seasonal trend can be predicted with multiple regression models and indicator variables or with Seasonal Exponential Smoothing. True or False?

True

If Q4 of 2018 occurred in t of 28, what quarter and year would t of 29 represent?

Q1 of 2019

What quarter and year would t of 32 be?

Q4 of 2019

Coefficient of Determination

R squared is the coefficient of determination. R squared explains the amount of variation in the independent variable.

What happens when you add more predictors to the model?

R squared will increase regardless whether the new predictors are good predictors. Adding predictors to a model that are not good predictors is the way that R squared can be artificially inflated. The sample size is not sufficiently large enough to handle the k predictors. 10 * k >= n is what we want to have.

What does the slope represent in a time series linear model?

The average rate of change in y over time.

Complete Second Order Model

A model that shows the independent variables with both squared values and interacted values

Second Order Model

A model that shows the independent variables with one of either squared values or interacted values.

First Order Model

A model that shows the independent variables without any squared values or interacted values.

Economic periods of prosperity followed by recession are described as:

Cyclical Variation

Residuals

The residual plot is shown to help us to determine if there are any issues with heteroscedasticity present. What we want to see are the residuals have equal variability on all levels of the change in the dependent variable (homoscedasticity). We don't want to see variation in the residuals changing as this indicates that we have a problem with heteroscedasticity. The residuals are the actual values of the dependent variable minus the predicted values of the dependent variable.

T test for individual coefficients

This test determines which independent variables are good predictors of the dependent variable. This is determined by looking at the p-values of each of these variables and if they are less than .05, they should be kept in the model as these are the good predictors.

R squared artificially inflated

We determine if R squared is artificially inflated by comparing the R squared and R squared adj. If there is a 10% difference, we have an issue with artificial inflation.

Interpret coefficient (Logistic Regression)

(Odd's Ratio - 1) * 100, as X increases by 1 unit, the odds of predicting y correctly, either increase if positive or decrease if negative by the percent, holding all other variables constant.

Secular Trend (Linear and Exp. Log)

A pattern in which the values of a time series tend to either increase or decrease over a long period of time. A straight line is often used to model the secular trend component of a time series. Some refer to the movement as a "smoothed" trend.

Seasonal Variation

A reoccurring pattern appears at the same time period each year.

F Test

An F Test is the process used to test the overall model to determine if we will accept the null hypothesis or the alternate hypothesis. The F-value is used as the test statistic.

How do you go about choosing between two different models with good predictors for y?

Choose the one with smallest standard error.

Name an industry that would have a seasonal component in its sales or revenue.

Christmas tree sales, Valentines, Swimsuits, Ski Items

Correlation Analysis

Correlation analysis is the process of taking a look at the correlation matrix and determining which independent variables are correlated with the dependent variable. You can also determine if there is any strong correlation between two independent variables which is called multicollinearity. You can determine whether there is a positive or negative correlation based on whether the number is positive or negative. If the number is less than 0.3, it is a weak correlation, if it is between 0.3 and 0.7, it is a moderate correlation, and if it is greater than 0.7, it is a strong correlation.

The merchants in South Carolina suffered flood damage in May 2015. Stores were closed for remodeling in for nearly 2 months. What is this type of variation in sales called?

Episodic Variation

Irregular Variation (Residual)

Events that are simply due to chance and cannot be identified or predicted.

Extrapolation

Extrapolating data is using values for x beyond the range of the observed x values. This can result in large errors in predictions.

Why is it important to check the signs of the coefficients?

If they are not logical, multicollinearity may be the culprit for this.

When do you use moving average, linear trendlines, exponential logs, and seasonal models? (Recognize the charts)

Moving average can be used to smooth out seasonal trends, show overall linear trends, or help smooth irregular trends. It is not as reliable because data is lost at the ends and should not be extended. When data slopes in a general up or down trend, use a linear equation. When data has regular (even widths) of waves each year, it has a seasonal trend.

Why is multicollinearity a bad thing?

Multicollinearity can mask good predictors and make the overall look good, but none of the predictors test be good.

Extrapolation Note

Never extrapolate data in multiple regression as this causes large errors in predictions. Time series is the one exception.

Important Note

Never say that x causes y unless it was a designed experiment.

Interpretation Priority Note

Only interpret the coefficients of good predictors and first order quantitative terms. First order terms are linear terms. Squared X's (quadratic terms) and interacted x's (x1 * x2) are called second order terms.

Testing the overall model (multiple regression)

Perform the F-Test using the ANOVA chart. Ho: B1 = B2 = B3 = ... = 0 Ha: At least one B is not 0 Test Statistic: F Ratio under ANOVA P-Value: Prob > F under ANOVA Conclusion: If p-value < .05, reject Ho

Logistic Regression

Predicts the outcome for a nominal variable.

What is Simple Moving Average?

Simple Moving Average is a smoothing technique that loses data at the ends. SMA and Exponential Smoothing are descriptive measures that smooth out data to reveal a secular trend.

Misclassification Rate

States the percent of values the model incorrectly predicted.

Root Mean Squared Error

The RSME is used when comparing two different models to determine which one is a better model for the dependent variable. The lower RSME shows the model that is better.

What is Mean Absolute Error (or deviation)?

The distance the residuals are from their mean of 0; it is the standard deviation of the residuals.

Heteroscedasticity

The issue that we see when looking at the residual plot that shows that the variability in the dependent variable changes at different values. If we have this we should take the log of the independent variable as this will help bring homoscedasticity back into the picture.

What happens when you re-run a model after taking out the poor predictor variables?

The model is REDUCED when you do this.

Studentized Residuals

These residuals are used to determine if there are any outliers in the model. If there is a studentized residual between 2 and 3, we have a suspicious outlier and if there is a studentized residual greater than 3, it is a severe outlier.

What should you do if there is a curve in the scatter diagram for any xy chart or in the residuals plot?

Use a quadratic equation. Use x and x squared or log of x.

What should you do if you think two variables may work together at different levels to affect y?

Use an interaction term like multiplying to x's together to form a new variable.

Testing individual coefficients to find good predictors (multiple regression)

Use t statistic and p-value under parameter estimates. If p-value for the specific variables is less than .05, this indicates that these are good predictors.

The equation using indicator variables is Y = B0 + B1t + B2Q1 + B3Q2 + B4Q3. What represents Q4 in the model?

When t is a multiple of 4, given the first Q1 occurs in time period 1, it will be a fourth quarter.