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Business Statistics Final Exam
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Terms in this set (51)
Dependent Variable
The variable that is being predicted or explained. It is denoted by y.
Independent Variable
The variable that is doing the predicting or explaining. It is denoted by x.
Simple Linear Regression
Regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line.
Regression Model
The equation that describes how y is related to x and an error term; in simple linear regression, the regression model is y=B0+B1x+E
Estimated Regression Equation
The estimate of the regression equation developed from sample data by using the least squares method. For simple linear regression, the estimated regression equation is y=b0+b1x.
Least Squares Method
A procedure used to develop the estimated regression equation. The objective is to minimize
E(yi-y(hat)i)^2
Scatter Diagram
A graph of bivariate data in which the independent variable is on the horizontal axis and the dependent variable is on the vertical axis.
Coefficient of Determination
A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.
Ith Residual
The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation; for the ith observation the ith residual is yi-y(hat)i
Correlation Coefficient
A measure of the strength of the linear relationship between two variables
Mean Square Error (MSE)
The unbiased estimate of the variance of the error term o^2 . It is denoted by MSE or s^2.
Standard Error of the Estimate
The square root of the mean square error, denoted by s. It is the estimate of o, the standard deviation of the error term e.
ANOVA table
The analysis of variance table used to summarize the computations associated with the F test for significance.
Confidence Interval
The interval estimate of the mean value of y for a given value of x.
Prediction Interval
The interval estimate of an individual value of y for a given value of x.
Residual Analysis
The analysis of the residuals used to determine whether the assumptions made about the regression model appear to be valid. Residual analysis is also used to identify outliers and influential observations.
Residual Plot
Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid.
Standardized Residual
The value obtained by dividing a residual by its standard deviation.
Outlier
A data point or observation that does not fit the trend shown by the remaining data.
Influential Observation
An observation that has a strong influence or effect on the regression results.
Time Series
A sequence of observations on a variable measured at successive points in time or over successive periods of time.
Time Series Plot
A graphical presentation of the relationship between time and the time series variable. Time is shown on the horizontal axis and the time series values are shown on the vertical axis.
Horizontal Pattern
A horizontal pattern exists when the data fluctuate around a constant mean.
Stationary Time Series
A time series whose statistical properties are independent of time. For a stationary time series the process generating the data has a constant mean and the variability of the time series is constant over time.
Trend Pattern
A trend pattern exists if the time series plot shows gradual shifts or movements to relatively higher or lower values over a longer period of time.
Seasonal Pattern
A seasonal pattern exists if the time series plot exhibits a repeating pattern over successive periods. The successive periods are often one-year intervals, which is where the name seasonal pattern comes from.
Cyclical Pattern
A cyclical pattern exists if the time series plot shows an alternating sequence of points below and above the trend line lasting more than one year.
Forecast Error
The difference between the actual time series value and the forecast.
Mean Absolute Error (MAE)
The average of the absolute values of the forecast errors.
Mean Squared Error (MSE)
The average of the sum of squared forecast errors.
Mean Absolute Percentage Error (MAPE)
The average of the absolute values of the percentage forecast errors.
Moving Averages
A forecasting method that uses the average of the most recent k data values in the time series as the forecast for the next period.
Weighted Moving Averages
A forecasting method that involves selecting a different weight for the most recent k data values values in the time series and then computing a weighted average of the values. The sum of the weights must equal one.
Exponential Smoothing
A forecasting method that uses a weighted average of past time series values as the forecast; it is a special case of the weighted moving averages method in which we select only one weight—the weight for the most recent observation.
Smoothing Constant
A parameter of the exponential smoothing model that provides the weight given to the most recent time series value in the calculation of the forecast value.
What is the expected value of y in a simple linear regression model?
Bo+B1x
Which of the following terms is used to describe an outlier with an extreme x value that strongly influences the regression analysis?
an influential observation
Which of the following represents the estimated regression equation that can be computed using sample data?
b0+b1x
(lowercase letters=sample data)
Which of the following types of relationships between a dependent variable y and an independent variable x is represented by a population regression line that resembles a horizontal line?
no linear relationship between the values of x and y
which of the following represents the slope in the equation y= 75 + 18x?
18
Which of the following terms represents the variation in a time series that appears to occur over the four seasons (summer, winter, spring and fall)?
the seasonal component
Which of the following would be most appropriate for making forecast accuracy comparisons across different time series?
a. Mean absolute percentage error
in the equation for a linear trend time series, Tt=bo+b1t, what does Tt represent?
linear trend forecast for period t
Horizontal Trend
-moving average
-exponential smoothing
Linear trend
-regression
In time series forecasting, x is
always a unit of time
Time series values are
the y-values
what is r2? (r squared)
Coefficient of correlation
-measures strength of relationship between x and y
-closer to 1=stronger relationship
-closer to 0=weaker relationship
example: .6= 60% of variation/noise is between dependent variable
-decimal
Standard Error
The standard deviation of a point estimator.
Why do we smooth out forecasts?
-cannot accurately predict with noise and variation
-try to smooth out variation and find line for data
Why we use Least Squares Method
-applied to regression analysis
-scatter plot
-try to find best fit line
-bo=y-intercept
-E=difference between best fit line and data point
-want to find line that minimizes noise, or distance between data point and line
-in equation, we assume we are finding perfect line, so average of E should equal zero
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