Chapter 7

Question 1

Representation of some phenomenon, which often describe relationships between variables.

Answer 1

Models

Question 2

What are two types of Models discussed?

Answer 2

Deterministic and Probabilistic.

Question 3

What type of model,

1. Hypothesize exact relationships.
2. Suitable when prediction error is negligible.
3. Example: Force is Exactly Mass times Acceleration.

Answer 3

Deterministic.

Question 4

What type of model,

1. Two Components with one component being a random error.
2. Y = 10X + Σ, where Σ represents a random error.

Note: Random Error may be due to factors other than advertising.

Answer 4

Probabilistic.

Question 5

There exist two types of Regression Models, each of which has two subsections, linear and non-linear. What are the two types of regression models?

Answer 5

Simple and Multiple.

Simple is what we will deal with in this class, higer courses in Statistics will deal with multiple.

Question 6

A simple linear regression model has a relationship between variables as a linear function. What is that function?

Answer 6

Y_i = ß₀ + ß₁X_i + Σ_i

Looks like the eqn. of a line with an additional component, random error.

Question 7

Describe what the least squares method technique is used for.

Answer 7

The technique is used to fit “the best fit” line through a set of ordered pairs where the residual squared is at the minimum.

Question 8

Define “best fit”.

Answer 8

The difference between actual Y values & Predicted Y values are a minimum.

Question 9

The difference between the observed value and its associated predicted value is called __________. The ___________ value tells us how far off the model’s prediction is at that point.

Answer 9

Residual.

Question 10

The line of best fit is the line for which the sum of the squared residuals is smallest, the ______ ________ line.

Answer 10

least squares, r.

Question 11

Consider the predicted least square equation.

ŷ = b₀ + b₁x

Now give it’s interpretation.

Answer 11

1. Slope (b₁)

For each 1 Unit Increase in X, estimated Y changes (increase/decrease) by b₁.

2. Y-intercept (b₀)

Average value of Y when X = 0.

Note: The Y-intercept may or may not make sense. This will depend on the range of the sample when X(0).

Question 12

Least squared lines are commonly called ___________ lines.

Answer 12

regression.

Question 13

The _________ __ ___________ or R² is an overall measure of how successful the regression is in linearly relating y to x.

Laymen terms: How effective your linear model ŷ.

Answer 13

Coefficient of Determination.

Question 14

What is the relationship of the linear coefficient (regression) and the coefficient of determination?

Answer 14

The coefficient of determination is the squared of the linear coefficent.

Question 15

The least squares concept does what to a simple linear regression model, in particularly to the random error?

Answer 15

Causes the residuals to become minimum.

Σ_i → 0.

Question 16

Given this solution, describe the interpretation.

r = 0.904 so R² = 0.817.

Answer 16

81.7% of the variability in (Y) is explained by (X).

Question 17

____________ ______ is a mathematical expression of some phenomenon.

Answer 17

Mathematical Model.