Introduction to Linear Regression - Reading 4

Question 1

What is a dependent variable?

Answer 1

the variable whose variation is explained bu the independent variable

Question 2

What are the six main assumptions underlying a simple linear regression?

Answer 2

1. A linear relationship exists between the dependent and the independent variables.
2. The independent variable is uncorrelated with the residuals.
3. The expected value of the residual term is zero.
4. The variance of the residual term is constant for all observations.
5. The residual term is independently distributed; that is, the residual for one observation is not correlated with that of another observation
6. The residual term is normally distributed.

Question 3

What is an independent variable?

Answer 3

the variable used to explain the variation of the dependent variable

Question 4

Which method is used to estimate a simple linear regression?

Answer 4

Minimizing the sum of squared errors

(Yi-^b0-^b1Xi)^2

Question 5

How to estimate b0?

Answer 5

^b0=Ym-^b1Xm

Question 6

How to estimate b1?

Answer 6

^b1=Cov(x,y)/Var(x)

Question 7

What is important to verify before any conclusions about the coefficients?

Answer 7

Determine the statistical significance

Question 8

What is the standard error of estimate (SEE) and how to calculate?

Answer 8

Measures the degree of variability of the actual y-values relative to the estimated Y- values from a regression equation
SEE=(SSE/n-2)^0,5
SEE=(MSE)^0,5

Question 9

What is the coefficient of determination and how to calculate?

Answer 9

tha percentage of the total variation in the dependent
variable explained by the independent variable
R^2=[(TotalVariation-UnexplainedVariation)]/Total Variation=ExplainedVariation/Total Variation

Question 10

What is the regression coefficient confidence?

Answer 10

Hypothesis testing for regression coefficient may use the confidence interval for the coefficient being tested.

Question 11

On regression coefficient intervals, what is the appropriate number of degrees of freedom?

Answer 11

n-k-1

Question 12

Formulate a null and alternative hypothesis about a population value of a regression coefficient

Answer 12

t=(^b-b_hypothesis)/Var(^b)

decision rule : reject H0 if t>tcritical or t

Question 13

What the rejection of the null means?

Answer 13

the rejection of the null means

that the slope coefficient is different from the hypothesised value of b

Question 14

What is the confidence interval for the predicted value?

Answer 14

ˆY+-(t_c x sf)

Question 15

how to calculate the variance error of the forecast?

Answer 15

sf^2=SEE^2{1+[1/n]+[(X-Xm)^2/(n-1)s_x^2]

Question 16

What is ANOVA?

Answer 16

Analysis of variance (ANOVA) is a statistical procedure for dividing the total variability of a variable into components that can la attributed to different sources

Question 17

What is the Total Sum of Squares (SST)?

Answer 17

Measures the total variation in the dependent variable

SST=sum(U-Ym)^2

Question 18

What is the Regression Sum of Squares (RSS)?

Answer 18

Measures the variation in the dependent variable that is explained by the independent variable
RSS=sum(Y^-Ym)ˆ2

Question 19

What is the decomposition of total variation?

Answer 19

SST=RSS+SSE

Question 20

What is the F-test? How to calculate the F statistic? How many df are in the numerator?How many df are in the denominator? Is it a two tailed or one-tailed?

Answer 20

An F-test assesses how well a set of independent variables, as a group, explains the variation in the dependent variable.
F=MSR/MSE=(RSS/k)/(SSE/n-k-1)
df_numerator=k
df_denominator=n-k-1
*this is always a one-tailed test
Decision rule: Reject h0 if F>F_c

Question 21

What is another way to calculate the F statistic more easily for a simple linear regression?

Answer 21

F=(t_b1)^2

Question 22

What are the three main limitations of regression analysis?

Answer 22

The main limilations of regression analysis include the following :

1. Parameter instability (especially when dealing with economic and financial variables).
2. The limited usefulness of regression models in identifying profitable investment strategies based on publicly available information
3. The possibility of violating the assumptions underlying regression analysis (heteroskedasticity and autocorrelation)