test 2 objectives

Briefly explain how to identify these effects.

Seasonal component- Short-term regular wave-like patterns. Observed within 1 year. Often monthly or quarterly Trend component: Long-run increase or decrease over time (overall upward or downward movement.) Data taken over a long period of time Cyclical Component: Long-term wave-like patterns. Regularly occur but may vary in length. Often measured peak to peak or trough to trough. Irregular Component: Unpredictable, random, "residual" fluctuations. Due to random variations of Nature. Accidents or unusual events. "Noise" in the time series.

Seasonal component

Short-term regular wave-like patterns. Observed within 1 year. Often monthly or quarterly

How do you test the slope in multiple regressions?

Test individual variables -Use t tests of individual variable slopes. -Shows if there is a linear relationship between the variable Xj and Y holding constant the effects of other X variables.

R2

The coefficient of determination is the portion of the total variation in the dependent variable that is explained by variation in the independent variable. The coefficient of determination is also called r-square and is denoted as r2.

dependent variable

The variable we wish to predict or explain

List and explain the four effects to be considered in time-series forecasting.

Trend, seasonal, cyclical, and irregular

State the main idea of Best Subsets Regression

Try all combinations and select the best using the highest adjusted r2 and Cp criteria. Estimate all possible regression equations using all possible combinations of independent variables.

Irregular Component

Unpredictable, random, "residual" fluctuations. Due to random variations of Nature. Accidents or unusual events. "Noise" in the time series.

In addition to trend smoothing, what is another advantage of exponential smoothing when compared to moving average?

Used for smoothing and short term forecasting (one period into the future.) A weighted moving average. Weights decline exponentially. Most recent observation is given the highest weight.

When is it appropriate to use multiple regression?

When using two or more independent variables to predict the value of a dependent variable.

What is the equation for a simple linear equation model?

Yi=B0+B1Xi+Ei

correlation analysis

a method of statistical evaluation used to study the strength of a relationship between two, numerically measured, continuous variables To see if there is a relationship between two numeric variables (R would tell us)

What are the two regression coefficients in the equation for the prediction line?

b0 & b1

How does the least-squares regression model work?

b0 and b1 are obtained by finding the values that minimize the sum of the squared differences between Y and Ŷ

What is the meaning of "Y-intercept"?

b0 is the estimated mean value of Y when the value of X is zero.

What is the meaning of the "slope" of a line?

b1 is the estimated change in the mean value of Y as a result of a one-unit increase in X.

Extrapolation

beyond the range of the plotted points

Yi

dependent variable

prediction interval

estimate for an individual value of Y given a particular Xi (for an individual Y, given Xi. )

confidence interval

estimate for the mean value of Y given a particular Xi

Xi

independent variable

coefficient of partial determination:

is the measure of the marginal contribution of each independent variable, given that other independent variables are in the model.

B0

population Y-intercept

What is the difference between r2 and adjusted r2?

r2 - Reports the proportion of total variation in Y explained by all X variables taken together. adjusted r2 - Shows the proportion of variation in Y explained by all X variables adjusted for the number of X variables used:

S

standard of error

R

the main result of a correlation

Interpolation

the region within the graph that contains the plotted variables

independent variable

the variable used to predict or explain the dependent variable.

What is the purpose of using "Dummy variables"?

-A dummy variable is a categorical independent variable with two levels: yes or no, on or off, male or female. (coded as 0 or 1) -Assumes the slopes associated with numerical independent variables do not change with the value for the categorical variable.

Explain the goal of model building in the case of multiple regression

-Goal is to develop a model with the best set of independent variables. -Model is easier to interpret if unimportant variables are removed. -Lower probability of collinearity

Give an example of a regression model using two independent variables.

A distributor of frozen dessert pies wants to evaluate factors thought to influence demand. Dependent variable: -Pie sales (units per week) Independent variables: -Price (in $) -Advertising ($100's)

When looking at a graph of residuals, how can you tell if a model is appropriate for the data?

By checking for violations Residual assumptions -The errors are normally distributed. -Errors have a constant variance. -The model errors are independent.

Explain how to smooth a time series model using moving averages.

Calculate moving averages to get an overall impression of the pattern of movement over time. Averages of consecutive time-series values for a chosen period of length L.

What are residuals?

Errors -The errors are normally distributed. -Errors have a constant variance. -The model errors are independent.

Which test statistic do you use to test the overall model in multiple regression?

F-statistic

Explain the meaning and use of VIF

If VIFj > 5, Xj is highly correlated with the other independent variables. (used to measure collinearity)

What are the three popular methods for trend-based forecasting?

Linear Trends: -Linear Trend Model. Non Linear Trends: -Quadratic Trend Model. -Exponential Trend Forecasting.

Trend component

Long-run increase or decrease over time (overall upward or downward movement.) Data taken over a long period of time

Cyclical Component

Long-term wave-like patterns. Regularly occur but may vary in length. Often measured peak to peak or trough to trough.

B1

Population slope coefficient

What is the purpose of regression analysis

Predict the value of a dependent variable based on the value of at least one independent variable Explain the impact of changes in an independent variable on the dependent variable -square root of R2(squared)

State the main idea of Stepwise Regression

Provide evaluation of alternative models as variables are added and deleted. Develop the least squares regression equation in steps. Add one independent variable at a time and evaluate whether existing variables should remain in the model or be removed.

Ei

Random error term