Exam Three

Question 1

Linear equation for one independent variable

Answer 1

Y= b0 + b1x

Question 2

First step to analysis

Answer 2

Constructing a graph of the data (scatterplot)

Question 3

Deterministic model

Answer 3

An exact relationship where there is 1 value of y for every x

Question 4

Probabilistic model

Answer 4

Allows for variability in y at each x value

Question 5

Least squares criterion

Answer 5

When multiple lines can fit scatterplot, the line with better fit is the one where the sum of the squared errors is smaller

Question 6

Calculating error (e)

Answer 6

1: find vertical distance between a line and a data point

2:sum of squared errors

Question 7

S(XX)

Answer 7

Sum of x(I) - mean (x) ^2

Question 8

S(xy)

Answer 8

Sum (xi-x bar)(yi-y-bar)^2

Question 9

S(yy)

Answer 9

Sum (yi-y bar)^2

Question 10

B1=

Answer 10

B1= sxy/sxx

Question 11

B0=

Answer 11

Mean y - b1 * mean x

Question 12

What do these equations help us do?

Answer 12

Find the regression equation

Question 13

How to examine the utility of a regression

Answer 13

Determine percentage of the variation in observed values of y that is explained by x (define both variation and amount of variation)

Question 14

SST

Answer 14

SST: sum of yi-y bar squared
This is a measure of total variation

Question 15

SSR

Answer 15

Sum of y hat - y bar squared
Measure of the amount of variation in the dependent variable explained by regression

Question 16

SSE

Answer 16

Yi- y hat i ^2
Variation in y NOT explained by the regression

Question 17

Relation between SST, SSR and SSE

Answer 17

SST = SSE + SSR
(Total = unexplained + explained)

Question 18

R^2 (coefficient of determination)

Answer 18

Percentage of variation in dependent explained by fitted regression

Between 0 and 1, near 0 means means it not useful, near 1 means it is

Question 19

R^2 equation

Answer 19

SSR/SST

Question 20

Coefficient of determination

Answer 20

Measure of how well outcomes are replicated by the model (r^2)

Question 21

MSE

Answer 21

Mean squared error. Estimates the average of the squares of errors

MSE= (1/n) sum of (yi - y hat)^2

Question 22

R

Answer 22

Aka: correlation coefficient

Measures how strong the linear relationship between x and y is. Ranges between -1 and 1. Strongest on either end, weakest close to 0

R= (sxy)/ sqrt (sxx * syy)
excel: = CORREL (column x, column y)

Question 23

Caution about correlation

Answer 23

Correlation can’t prove causation: strong correlation can be produced by chance, effect of 3rd variable, etc.
Near 0 correlation may just mean the variables don’t have a linear relationship.
Outliers can also affect correlation

Question 24

Purpose of sample regression

Answer 24

To predict a population regression