BA 4 - Single Variable Linear Regression

Question 1

Regression, linear regression, single variable linear regression

Answer 1

Regression - examines the relationship among variables

Linear regression - examines linear relationships among variables

Single variable linear regression - seeks to identify a linear relationship between two variables

Question 2

Uses of regression

Answer 2

Primary uses:

i. Studying the magnitude and structure of a relationship between two variables; and
ii. Forecasting a variable based on its relationship with another variable.

Question 3

Regression equation

Answer 3

y^ = a + bx

y is the dependent variable, x is the independent variable, a is the y-intercept, b is the slope

true eq: y = alpha + (beta)x + epsilon

Question 4

Point forecast

Answer 4

The value of y determined by entering the particular value of x into the regression equation

Question 5

Prediction interval

Answer 5

Interval around the point forecast likely to contain the actual value of y.

The width of the prediction interval is based on the:

i. sd of the regression;
ii. the desired level of confidence; and
iii. the location of the x-value in relation to the historical values of the independent variable.

Question 6

R^2

Answer 6

R^2 = (Regression sum of squares)/(Total sum of squares)

i.e. variation explained by the regression line divided by the total variation.

0 =< R^2 =< 1

Question 7

p-value

Answer 7

result of the hypothesis test on whether there is a significant linear relationship - i.e. whether the slope of the regression line is zero
H0: beta = 0; Ha: beta =/= 0

If p<= 0.5 and if the confidence interval doesn’t contain zero we fail to accept H0.

Question 8

Residual, regression and total sum of squares

Answer 8

Residual - variation unexplained by the regression equation

Regression - variation explained by the regression equation

Total - variation around the mean line

Question 9

To check in residual plot

Answer 9

Residuals should be randomly spread above and below the x-axis.
Pattern implies other factors are at play.

Question 10

To know if SVLR is the right fit

Answer 10

R^2
p-value
residual plot

Question 11

Regression analysis with categorical variables

Answer 11

Use a dummy variable

Question 12

[EXCEL] Value of y

Answer 12

=CELL1+CELL2*x

for y=a + bx

Question 13

[EXCEL] To calculate point forecasts

Answer 13

=SUMPRODUCT(array1,[array2],[array3]…)

Question 14

[EXCEL] To forecast value

Answer 14

=FORECAST(x, known_ys, known_xs)

dependent array, independent array

Question 15

[EXCEL] Regression models with dummy variables

Answer 15

=IF(logical_test,[value_if_true],[value_if_false])