Section 2 Math & Stats Flashcards
Operating Expense Ratio + Net Income Ratio
= 100%
Demand Curve has what relationship & slope
Inverse relationship, negative slope
Supply curve has what relationship & slope?
Direct relationship & a positive slope
What are the three ways to express change?
total, average annual, annually compounded
How do you measure change?
opinions of market participants, published data, aggregated data, extrapolation, paired data analysis, sorting data, graphing data, regression analysis linear or logarthims
How do you calculate change?
End#/Start# -1
Measures of Central Tendency
spectrum of all numbers where the population clusters
Measures of Dispersion
how widely is the data spread out
What is the mean? why is it not useful (con)
Average, affected by outliers
Median
the one in the middle
how do you solve for the mean on the hp
enter each number w/ sigma+ then calculate for the blue key on 0 (x w/ a line over it)
how do you solve for standard deviation on the hp
enter each number w/ sigma+ then g s (blue of the .)
What is the median? why isn’t it useful? what’s the formula
the one in the middle N+1/2, isn’t useful because it isn’t calculated
What is the mode? why isn’t it useful? what’s the formula
most frequently occuring observation, more than one mode, observed not calculated
What is the central tendency in a normal distribution?
68% 1 SD, 95% 2 SD, 99% 3 SDs
What is the central tendency in a non -normal distribution?
50% 1.4 SDs (not useful) 75% 2 SDs, 89% 3 SDs, 94% 4 SDs
What are 3 measures of dispersion
Range, Standard Deviation, Coefficient of Variation COV
How do you calculate dispersion in a range? What are the cons?
End #/Begin# -1 (expressed as a number not a percent .201 as 201 not 20.1%, doesn’t consider in between numbers, doesn’t consider all data
What is the standard deviation? How do you calculate it? what are the cons?
An approximation of the average distance of each item from the mean, with your HP!, need a computer or calc. With HP enter all data with Sigma +, calc gs on blue . key
What is the Coefficient of Variation? How do you calculate it?
a measure of dispersion as a percentage. A lower COV has less risk & is more reliable, SD/Average
Which axis has the dependent variable?
Y axis (usually price or value)
Which axis has the independent variable?
X axis (usually size, units etc.)
What does the slope of the line represent?
The per unit adjustment
If the slope is -1 to 0 what does that tell you?
Inverse relationship, negative slope, demand curve
If the slope is 0 to 1 what does that tell you
Direct relationship, positive slope, supply curve
What is it called when you extend the trend line past the last data point?
Extrapolation
Trendlines are placed so the sum of the squared residuals is the smallest possible, what is this called?
Least Squared Error
How do you calculate the least squared error
measure the distance between each data point and the trend line, square each distance, add all the squared distances, the best fit line has the leased squared differences
Regression model
used to precisely place a trendline.
Linear regression model
straight trend line, Y = mx +b
What does y=mx+b calculate? What do the letters stand for?
Linear regression model. Y - the answer on the Y axis (value). b - the y intercept (place the line crosses y), m - slope of the line calculated as the change in x / change in y (per unit adjustment), x any number on the x axis
How do you calculate m in a linear regression model?
m - slope of the line calculated as the change in x / change in y (per unit adjustment) (Y=mx+b)
How do you do regression w/ a 12C?
y enter x sigma plus for all variables then take an x variable g yhat - (blue2) - use another x variable to get a change per period or per unit calculate that change per period - to get the slope, x><y key to get the correlation coeffieient r.
what is r in regression?
correlation coeffiecient
what is R2
Coefficient of determination
What is a correlation coefficient?
r, indicates the direction of the slope either plus or minus + direct, - indirect
What is the coefficient of determination?
R squared or multiple R, measures how well the whole model explains differences in the dependent variable
Should you eliminate an outlier in regression?
not unless you know what causes it to be inconsistent or if the subject doesn’t have the same atypical characteristic
when should you use a short trend?
when one part of the data set is more relevent than the rest
What kind of trend lines do appraisers use? (4)
Straight line, polynomial (hills & valleys), power (curve that increases or decreases in an increasing or decreasing rate), exponential (%)
Do measures of central tendency depict trends?
no
When is regression a better predictive tool?
when the data does have a pattern
regression analysis is similar to what other quantitative appraisal technique?
paired sales data
a line with minimal slope indicates what?
a minimal adjustment
for a normal distribution what can be said about the measures of central tendency?
all 3 measures are the same
what is the model for a straight trend line?
y = mx+b
what do you know about the slope for a straight line
it is constant, doesn’t change
How are r and Rsquared related and what are their proper names?
The Rsquared is the Coeffiecient of Determination and it is the square of r the correlation coefficient
As extrapolation increases what also increases
Risk
what do zero residuals mean in a trend line?
all the data points are on the line
what is the difference between the data points and the trend line called?
regression error or residual
how do you caluculate the volume of a silo?
pi x r squared x height divided by cubic yards in a bushel. (they seem to provide this) (4.7 bushels of corn in a cubic yard = 27 cu ft. a bushel of corn requires 2.5 cubic feet in examples)
how do you calculate the area of a spandral
area of the square - area of the circle / 4
how do you calculate the perimeter of a spandral?
perimeter of a square x 25% + circumference of a circle x 25%. (Circumference of a circle is pi * diameter)
