Stats

Question 1

What is an index?

Answer 1

A change compared to a base value expressed in %.
Eg. Today $ / 2006 $ (x100) = 140
Equivalent to a 40% increase over 2006

Question 2

Compare/contrast percentage vs. Index

Answer 2

Percentages compare only to its own point of reference. Index standardize the point of reference.

Question 3

Absolute vs. Relative frequencies

Answer 3

Absolute is exact numbers. Relative is numbers within a range. Eg. 10-20

Question 4

Line graph vs. Histogram

Answer 4

Line for relative frequencies
Bar centered on center point of range for frequency, touching other bars

Question 5

EQ: mean (what, how to calc)

Answer 5

Sum / # of entries

Gives average value

E+, then x,y key

Question 6

EQ: weighted arithmetic mean

Answer 6

Sum of (variable x weight) / sum of weights

Gives average

Question 7

Mean vs median

Answer 7

Mean higher than median means bulk of data is lower and there is a right side tail (high potential outliers)

Mean lower than median means bulk of data is higher and there is a left side tail (low potential outliers)

Question 8

When is mode useful?

Answer 8

Non-numeric data. Eg. Fav colours

Question 9

EQ: Standard deviation

Answer 9

Looks like o with a tail

Value - mean, square it, sum them,divide by n, square root it

Gives how tightly clustered the values are. High = flat curve (loose)

Calc: sum values then ox, oy

Question 10

Standard deviation intervals for a normal distribution

Answer 10

1 = 68.27%
2 = 95.45%
3 = 99.73%

Question 11

EQ: Variance

Answer 11

Sum of (value - mean)^2 / n
OR std dev squared

Not very useful

Question 12

EQ: coefficient of variation

Answer 12

SINGLE VARIABLE
= std dev / mean x 100
Shows how big the standard deviation is compared to the mean. Larger means more dispursed or more variable

BIVARIATE
=SEE / mean (dependent variable) x 100
tells us the size of the error as compared to the mean (%)

MULTIVARIATE
=same as bivariate

Question 13

When is the median preferable to the mean?

Answer 13

1. Open-ended frequency group
2. Extreme values

Question 14

EQ: Linear correlation coefficient (r)

Answer 14

Shows relationship between tow variables. Value from -1 to 1. Zero means no correlation. r > 0.8 strong, r < 0.4 weak.

BIVARIATE

Calc: x1 INPUT y1 [E+], [x^,r] ,SWAP

Cons: cannot describe non-linear relationships

Multivariate counterpart is coefficient of determination (R^2)

Question 15

EQ: Sum of least squares (S)

Answer 15

BIVARIATE

(Actual - predicted)^2, then sum

Univariate would be variance before dividing by n

Question 16

How to solve for bivariate linear equasion

Answer 16

x INPUT y [E+]
0 [y^,m] gives y-intercept
SWAP gives slope

Question 17

EQ: Standard error of the estimates (Syx) or (SEE)

Answer 17

BIVARIATE is Syx

Equasion 11.7
Suggests prediction error. Is in the same unit as the variable. Lower is better
MULTIVARIATE
also known as Root Mean Square Error
Analogous to standard deviation of regression errors, same % for normal distribution (68.27%, 95.45%, 99.79%). Shows how scattered. Low = close

Question 18

How do you turn a non-numerical variable into a number?

Answer 18

Turn each option into a yes(1)/no(0)

Question 19

What are the four “goodness of fit” variables?

Answer 19

Coefficient of determination (R^2)
Standard error of the estimate (SEE)
Coefficient of variation (COV)
F-value

Question 20

What are the two statistics that relate to the importance of individual variables?

Answer 20

Correlation coefficient (r)
t-statistic

Question 21

EQ: coefficient of determination (R^2) and adjusted R^2

Answer 21

MULTIVARIATE
=correlation coefficient (r) squared
Shows how well the regression model explains the variation in the dependent variable in %. 0 (low) to 1 (high).
Weaknesses:
1. can only go higher with more variables added. Goodness of fit could be overstated by adding many insignificant variables. (Corrected by using adjusted R^2)
2. Every model is different, so no benchmarks for fit.

Question 22

To improve multiple regression model, what should you look at?

Answer 22

First, SEE and COV, then R2

Question 23

What are strata and what it the effect on R2?

Answer 23

Strata are groups made before modeling. Then each group gets a model. Eg. Neighbourhoods.

R2 may be less because a large part of the variation is removed already by the strata. What is left to be modeled forms the new basis for R2

Question 24

EQ: f-value
(formula, meaning, benchmark, weakness)

Answer 24

= variance explained by regression divided by unexplained by regression

Is the model useful or no more useful than using the mean?

Tests whether model is NOT sufficient. F<4 = not significant
F>4=significant

Sensitive to number of variables/observations. High variables with low observations generally give f<4

Question 25

EQ: t-statistic

Answer 25

Confidence. How sure are we that the coefficient is NOT zero? Bigger=better. Outside of +-2.58 = 99% Outside of +-1.96 = 95% Outside of +-1.64 = 90% Significance level 0.10 means 90% confident it is not zero. 0.05 is reliable.

Question 26

Quick check list regression outputs:

Answer 26

- Coefficients have expected signs - t-stat outside +-1.64, significance less than 0.10 - f-value greater than 4 - SEE approaching zero - COV less than 20%, under 10 ideal - adjusted R close to 1 (above 0.8)

Question 27

EQ: aggregate ratio

Answer 27

= sum of assessment / sum of sale Susceptible to sampling error, high outliers. (versus mean ASR which is sum of (assessment/sale) divided by n. and gives all observations equal weight.

Question 28

Explain percentiles and quartiles

Answer 28

Dividing points in a data set. Median is 50th percentile and 2nd quartile

Question 29

EQ: average absolute deviation (AAD)

Answer 29

=(ASR - median) sum absolute values, divide by n Gives average spread similar to std dev but with median

Question 30

EQ: coefficient of dispersion (Formula, benchmark, weakness)

Answer 30

=AAD / median Makes comparable across groups Good is 15 or less Weakness: Cannot state probability of accuracy of a given assessment

Question 31

EQ: price related differential (PRD) (formula, interpretation, benchmark)

Answer 31

= mean ASR divided by aggregate ratio of ASR Greater than 1.00 means high$ properties under appraised (regressive) Less than 1.00 means progressive (overassessed) Optimim: 0.98 <> 1.03

Question 32

IAAO standards (ASR, COD)

Answer 32

- ASR 0.90 <> 1.10 - Each stratum should be within 5% of overall for stratum - SF res should be COD 5 <> 15 - ICI should be COD 5 <> 20 - vacant land COD 5 <> 25

Question 33

Standard error of the mean (o-x)

Answer 33

O-x = o pop/sqrt n