Calculate a Mutiple Regression Problem.

¶ … calculate a mutiple regression problem. All that you need are some variables and observations. Your assignment is to calculate and interpret a three-variable regression model, having a single dependent variable and two indepedent varaibles.

Y = a + b1X1 + b2X2

You will be predicting the percentage of vote for the incumbent president as the dependent variable and his popularity and the unemployment rate as indepedent variables. The data is provided below.

Vote Share Popularity Unemployment

Go to the site below and CAREFULLY READ the DIRECTIONS. Plug your data into the sheet, filling out columns X1 (popularity) and X2 (unemployment) for the independent variables and Y (vote share) for the dependent variable. Click "Calculate" at the top of the table. This will give you the regression line. After you get the results, provide an interpretation of the intercept (a) and the two regression coefficients (b). GOOD LUCK!

Multiple Regression

http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/MultRgression.htm

The Fitted Model is:

X1

X2

X3

X4

Y

Predicted

Y values

Diagnostic Tools for Data Transformation Decisions

R-Square

F-Statistic

Mean

Variance

Mean:

The first half

Mean:

The second half

Variance:

The first-half

Variance:

The second half

First order serial-correlation

Second order serial-correlation

Durbin-Watson statistic

Mean absolute errors

Normality Condition:

ith Residual:

Answer:

Y = 40.58 + (0.3406)X1 + (-1.147)X2

Vote share is the dependent variable that depends on popularity and unemployment. Assessment is made and predicted of how contingent the politician's vote is on the other two variables. Namely, to which extent his or her popularity and the climate of employment will predict his gaining seats in Party

Vote share = 40.58 + (0.3406)popularity + (-1.147)unemployment

This means that his votes tally to almost 41% of the population. His popularity index is 34% and the unemployment ratio is 114% in a negative direction.

This can now be graphed to see prediction of the degree to which unemployment and popularity effects votes accorded politician and to see the chance that he stands.

2) Assignment - Scatterplots - Scatterplots ( Please see upload) - {Approximately 2 pages to answer 3 questions}

1. What is the equation for a regression line? What does each term in the line refer to?

Answer:

Y' = bX + a, x is the independent variable (that plotted on the horizontal line), b is the slope of the line and a is the y intercept (i.e. The point on the line where x intercepts with y (the variable graphed on the vertical line / the dependent variable). Y' consists of the predicted values of Y for the various values of x.

2. If a regression equation were: Y = 3X + 5, what would be the predicted score for a person scoring 8 on X?

Answer:

Y = 3X * 8 + 5 =29

3. Generally speaking, during presidential election years, the winning candidate's party gain seats in the House of Representatives. However, during the off-year or midterm election, the president's party losses seats in the House. The number of seats that the president's party losses often depends on how popular he is with the voters. Use the regression equation provided below to predict the number of seats the Republican party will loss (or win) in the House, where:

Y = number of seats

X = the president's approval rating (the percentage of voters who think that he is doing a good job as president).

Answer:

Y = -9.75 + .15X = -9.6