Stats Final
Rejection Rule F test
Reject if calculated F is greater than table F
Recurring patterns over successive periods of time , can be less than one year
Seasonal pattern
if the most recent values of the time series are considered relevent then what type of k do we want?
Smaller
If the f test shows overall significance, than the BLANK test is used to determine whether each of the individual independent variables is significant.
T
Gradual shift or movement to relatively higher or lower values over a long period of time. usually a result of long term factors such as population shifts etc
Trend pattern
To test for a significant relationship we need to conduct a hypothesis test to determine whether the value of B1 is zero or not T or F?
True
correlation coefficient captures only linear relationships T or F?
True
forecast is based solely on on past values of the variable and/or past forecast errors T or F?
True
in multipl regression the interpretation of slopes b1 through bk only denote "partial" influence T or F?
True
the correlation coefficient may not be a reliable measure if outliers exist? T or F?
True
the explanatory variable(x) influences the response variable(y) and is never reversed in a simple linear regression model. T or F?
True
there is always a possibility that some 3rd lurking variable is simultaneously affecting both of the variables you have observed? T or F?(correlation analysis)
True
when independent variables are highly correlated it is not possible to determine the separate effect of any particular variable on the dependent variable? T or F?
True
A least squares regression line ______. a. may be used to predict a value of y if the corresponding x value is given b. implies a cause-effect relationship between x and y c. can only be determined if a good linear relationship exists between x and y d. All of these answers are correct.
a. may be used to predict a value of y if the corresponding x-value is given
Regression analysis is a statistical procedure for developing a mathematical equation that describes how _____. a. several independent and several dependent variables are related b. one independent and one or more dependent variables are related c. one dependent and one or more independent variables are related d. None of these answers are correct.
c. one dependent and one or more independent variables are related
the regression model assumes that the mean of the y values for each value of x fall...
exactly on the same line
overall significance
f test
multiple regression model explaining power is...
higher then single/simple regression models
Sxy(covariance)
sum of (xi- x mean)(yi-y mean)/n-1
Rxy(correlation coefficeint)
sxy/(standard dev x)(standard dev y)
individual significance
t test
A sequence of observations on a variable measured at successive points in time or over successive periods of time.
time series data
goal of time series data analysis
to discover a pattern and then extrapolate the pattern into the future
a smaller k value will....
track shifts in a time series more quickly
the proportion of the variance in the dependent variable that is predictable from the independent variable. Answers how well the estimated regression equation fits the data(goodness of fit)
Coefficient of determination (r squared)
indicates both the direction and strength of the linear relationship. Ranges bwtween -1 and +1, has no units
Correlation Coefficient (rxy?)
uses a weighted average of past time series vlaues as a forecast
Exponential Smoothing
If two variable are highly correlated that means one causes the other T or F?
False
If we add more independent variables , then our regression model explains worse? T or F?
False
difference between the actual and the forecasted values for period T
Forecast error
F test null and alternative hypothesis
Ho: B1= 0 Ha: b1 does not equal 0
exists when the data fluctuates randomly around a constant mean over time. Stationary time series denotes a time series whose statistical properties are independent of time. a timer series plot for stationary time series will always exhibit this pattern
Horizontal pattern
(MSE) avoids the problem of positive and negative forecast errors from offsetting one another
Mean Squared error
(MAE) avoids the problem of positive and negative forecast errors from offsetting one another
Mean absolute error
MFE
Mean forecast error
correlation among independent variables
Multicollinearity
using the most recent data to predict future data
Naive forecasting method
used whenever we want to predict an individual value of y for a new observation corresponding to a given value of X
Prediction interval
a BLANK line is a description of the data and its trend
Regression
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____. a. a residual b. a prediction interval c. the standard error d. the variance
a. Residual
The interval estimate of the mean value of y for a given value of x is the _____. a. confidence interval b. correlation interval c. residual interval d. prediction interval
a. confidence interval
If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the estimated regression equation _____. a. can be any positive value b. is 16% c. is 4% d. is 40%
b. is 16%
If a greater number of past values are considered relevant then what size k do we want?
bigger
A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: ŷ = 50,000 + 6x The above equation implies that an increase of _____. a. $1 in advertising is associated with an increase of $6 in sales b. $1 in advertising is associated with an increase of $56,000 in sales c. $1 in advertising is associated with an increase of $6,000 in sales d. $6 in advertising is associated with an increase of $6,000 in sales
c. $1 in adverting is associated with a increase of 6000 in sales
a numerical measure that reveals the direction of the linear relationship between two variables
covariance (Sxy?)
simple regression b1 is..
covariance of x and y / variance of x
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the _____. a. standard error of the estimate b. correlation coefficient c. confidence interval estimate d. coefficient of determination
d. coefficient of determination
A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: ŷ = 9 − 3x The above equation implies that if the price is increased by $1, the demand is expected to _____. a. decrease by 3 units b. decrease by 3,000 units c. increase by 6 units d. decrease by 6,000 units
decrease by 3,000 units
A larger k value will be....
more effective in smoothing out random fluctuations
a linear regression model that consists of 2 or more explanatory variables to explain the variation in the response variable. Allow us to explore how several variables influence the response variable
multiple linear regression model
If there is more than one explanatory variable we can use a...
multiple regression