Book 1_Quan_Simple Linear Regression

Question 1

Linear regression definition

Answer 1

provides an estimate of the linear relationship between an
independent variable (the explanatory variable) and a dependent variable (the
predicted variable)

Question 2

The general form of a simple linear regression model

Answer 2

• Yi = bo + b1 Xi + ei
  + b1 = fitted slope coefficient = COVxy/stdx^2
  + b0 = fitted intercept = Y – b1 X

+ Dependent variable: Y
+ Independent variable: X

Question 3

The estimated intercept, b0

Answer 3

represents the value of the dependent variable at the
point of intersection of the regression line and the axis of the dependent variable
(usually, the vertical axis)

Question 4

The estimated slope coefficient, b1

Answer 4

is interpreted as the
change in the dependent variable for a one-unit change in the independent variable.

Question 5

Assumptions made regarding simple linear regression include the following:

Answer 5

1. A linear relationship exists between the dependent and the independent variable.
2. The variance of the residual term is constant (homoskedasticity).
3. The residual term is independently distributed (residuals are uncorrelated).
4. The residual term is normally distributed.

Question 6

Linear Relationship

Answer 6

A linear regression model is not appropriate when the underlying relationship
between X and Y is nonlinear

Question 7

Homoskedasticity

Answer 7

refers to the case where prediction errors all have the same variance

Question 8

Normality

Answer 8

When the residuals (prediction errors) are normally distributed, we can conduct hypothesis testing for evaluating the goodness of fit of the model

Question 9

Outliers

Answer 9

observations (one or a few) that are far from our regression line (have
large prediction errors or X values that are far from the others)

Question 10

Analysis of variance (ANOVA)

Answer 10

a statistical procedure for analyzing the total
variability of the dependent variable.

Question 11

The total sum of squares (SST)

Answer 11

measures the total variation in the dependent
variable

SST = total (Yi – Ymean)^2

Question 12

The mean square regression (MSR)

Answer 12

the SSR divided by the number of independent variables

(MSR) = RSS/k

Question 12

The sum of squares regression (SSR)

Answer 12

measures the variation in the dependent variable that is explained by the independent variable

RSS = total (expected Yi – Ymean)^2

Question 13

The sum of squared errors (SSE)

Answer 13

measures the unexplained variation in the
dependent variable

total (Yi – expected Yi)^2

Question 14

The mean squared error (MSE)

Answer 14

is the SSE divided by the degrees of freedom,
which is n − 1 minus the number of independent variables

(MSE) = SSE/(n-k-1)

Question 15

Total variance formula

Answer 15

total variation = explained variation + unexplained variation
or:
SST = SSR + SSE

Question 16

Standard Error of Estimate (SEE)

Answer 16

is the standard deviation of its residuals. The lower the SEE, the better the model fit:

(SEE) = căn (MSE)

Measure the degree of variability of the actual Y values relative to the estimated Y values from a regression equation

Question 17

Coefficient of Determination (R2)

Answer 17

The percentage of the variation of the dependent variable that is explained by the independent variable

= SSR/SST => Càng lớn thì đường regression càng đúng

Question 18

An F-test meaning

Answer 18

• assesses how well a set of independent variables, as a group, explains the
  variation in the dependent variable
  or
• evaluate whether independent variable explain the variance of dependent variable

o Ho: b1 = 0; Ha: b1 # 0
o One-tailed test
o F = MSR/MSE
o Critical value: depend on the level of significant and and 2 degrees of freedom: k and n – k – 1
o Reject Ho nếu F-statistic > Critical value

Question 19

Hypothesis Test of a Regression Coefficient

Answer 19

o Slope coefficient (b1^): Tb1 = (b1^ - b1)/Sb1
o Pair-wise correlation (p)
o Intercept (bo^)
o Two-tailed statistic

Question 20

Confidence Intervals for Predicted Values

Answer 20

o Y^ +- (tc x st)
o tc = two-tailed critical t-value at the desired level of significance with df = n-2
o sf = standard error of the forecast

Question 21

Log-lin model

Answer 21

This is if the dependent variable is logarithmic, while the independent variable is linear.

Question 22

Lin-log model

Answer 22

This is if the dependent variable is linear, while the independent
variable is logarithmic

Question 23

Log-log model

Answer 23

Both the dependent variable and the independent variable are
logarithmic.