week 4

Question 1

what are trends?

Answer 1

they are part of predictive analysis, used to understand any relationships between one or more variables
- Functional relationships can be converted into analytical models

Question 2

what are the three types of functions used in predictive analysis?

Answer 2

1. Linear function: y = a + bx . Linear functions show steady increases or decreases over the range of x . This is the simplest type of function used in predictive ­ models. It is easy to understand, and over small ranges of values, can approximate behaviour rather well.
2. Logarithmic function: y = ln 1 x 2 . Logarithmic functions are used when the rate of change in a variable increases or decreases quickly and then levels out, such as with diminishing returns to scale. often used in marketing models where constant percentage increases in advertising, 3, Polynomial function: y = ax 2 + bx + c (second order— quadratic function), y = ax 3 + bx 2 + dx + e (third order— cubic function), and so on. A second order polynomial is parabolic in nature and has only one hill or valley; a third order polynomial has one or two hills or valleys. Revenue models that incorporate price elasticity are often polynomial functions.

Question 3

what are the other two functions in predicative analysis?

Answer 3

4. Power function: y = ax b . Power functions define phenomena that increase at a specific rate. Learning curves that express improving times in performing a task are often modeled with power functions having a 7 0 and b 6 0. Exponential function: y = ab x .
5. Exponential functions have the property that y rises or falls at constantly increasing rates. For example, the perceived brightness of a lightbulb grows at a decreasing rate as the wattage increases. In this case, a would be a positive number and b would be between 0 and 1. The exponential function is often defined as y = ae x , where b = e , the base of natural logarithms (approximately 2.71828).

Question 4

what is regression analysis?

Answer 4

Regression analysis is a tool for building mathematical and statistical models that characterize relationships between a dependent variable (which must be a ratio variable and not categorical) and one or more independent, or explanatory, variables, all of which are numerical (but may be either ratio or categorical).

Question 5

what are the two types of regression model?

Answer 5

(1) regression models of cross-sectional data and
(2) regression models of time-series data, in which the independent variables are time or some function of time and the focus is on predicting the future.

Question 6

what is simple linear regression?

Answer 6

involves finding a linear relationship between one independent variable X and one dependent variable Y.

Question 7

what is the problem with errors in simple linear regression?

Answer 7

Simply summing up the errors may result in some
cancelling each other out
- We instead sum up either the absolute values or squares:
least squares regression
- done in excel

Question 8

what is a multiple linear regression?

Answer 8

a linear regression model with more than one independent variable
- we estimate partial regression coefficients

Question 9

what are the assumptions about the data in regression analysis?

Answer 9

1. Normality of errors . Regression analysis assumes that the errors for each individual value of X are normally distributed, with a mean of zero. This can be verified either by examining a histogram of the standard residuals and inspecting for a bell-shaped distribution or by using more formal goodness-of- fit tests. It is usually difficult to evaluate normality with small sample sizes.

Question 10

what is homoscedasticity?

Answer 10

another assumption of the data in regression analysis which means that the variation about the regression line is constant for all values of the independent variable.
- points should be randomly scattered no pattern

Question 11

what is independence of errors?

Answer 11

another assumption of data in regression analysis, which means one observation is independent on one another which gives correlation which we dont want in regression analysis. each observation should be as uncorrelated to each other as possible

Question 12

what is autocorrelation?

Answer 12

its the correlation among successive observations over time and can be found with residual plots having clusters of residuals with the same signs

Question 13

what does residual mean?

Answer 13

The difference between an observed value of the response variable and the value of the response variable predicted from the regression line.

Question 14

what is r2 (r-squared)?

Answer 14

r-squared shows how well the data fit the regression model (the goodness of fit)
value is between 0 and 1.
the larger the R2 value the better the fit

Question 15

what is historical analogy?

Answer 15

its a judgemental technique in which a forecast is obtained through a comparative analysis with a previous situation

Question 16

what is the delphi method?

Answer 16

another judgemental approach uses a panel of experts whose are identities are usually private, to respond to a sequence of questionnaires

Question 17

what are indicators or indexes?

Answer 17

• Indicators are measures that are believed to influence the behavior of a variable we wish to forecast. By monitoring changes in indicators, we expect to gain insight about the future behavior of the variable to help forecast the future.
• Indicators are often combined quantitatively into an index , a single measure that weights multiple indicators, thus providing a measure of overall expectation.

Question 18

what is time series?

Answer 18

its a type of statistical forecasting model that is stream of historical data such as weekly sales, the model assumes that whatever forces have been influenced sales in the recent past will do so in the future

Question 19

what does time series usually have and not have?

Answer 19

Time series generally have one or more of the following components: random behavior, trends, seasonal effects, or cyclical effects. Time series that do not have trend, seasonal, or cyclical effects but are relatively constant and exhibit only random behavior are called stationary time series.

Question 20

what is a seasonal and cyclical effect?

Answer 20

Time series may also exhibit short-term seasonal effects (over a year, month, week, or even a day) as well as longer-term cyclical effects, or nonlinear trends. A seasonal effect is one that repeats at fixed intervals of time, typically a year, month, week, or day.
- Cyclical effects describe ups and downs over a much longer time frame, such as several years

Question 21

what is simple moving average?

Answer 21

The simple moving average method is a smoothing method based on the idea of averaging random fluctuations in the time series to identify the underlying direction in which the time series is changing. Because the moving average method assumes that future observations will be similar to the recent past, it is most useful as a short-range forecasting method.

Question 22

how do we analyse the effectiveness of different forecasting models?

Answer 22

we can define error metrics , which compare quantitatively the forecast with the actual observations. Three metrics that are commonly used are the mean absolute deviation , mean square error , and ‘mean absolute percentage error . The ‘mean absolute deviation’ (MAD) is the absolute difference between the actual value and the forecast, averaged over a range of forecasted values:

Question 23

what is the simple exponential smoothing?

Answer 23

is a time series forecasting method for univariate data without a trend or seasonality. It requires a single parameter, called alpha (a), also called the smoothing factor or smoothing coefficient.

Question 24

what happens due to our assumption of a linear relationship in the simple linear regression model?

Answer 24

Because we are assuming that a linear relationship exists, the expected value of Y is b 0 + b 1 X for each value of X . The coefficients b 0 and b 1 are population parameters that represent the intercept and slope, respectively, of the population from which a sample of observations is taken.
- The intercept is the mean value of Y when X = 0, and the slope is the change in the mean value of Y as X changes by one unit. Thus, for a specific value of X , we have many possible values of Y that vary around the mean. To account for this, we add an error term, e

Question 25

what should the best fitting line in simple linear regression modelling do?

Answer 25

The best-fitting line should minimize some measure of these errors. Because some errors will be negative and others positive, we might take their absolute value or simply square them. Mathematically, it is easier to work with the squares of the errors. - - If we can find the best values of the slope and intercept that minimize the sum of squares (hence the name “least squares”) of the observed errors e i , we will have found the best fitting regression line.