# Regression and Linear Trend Equations

1. I would like to a use the regression equation: Y'= a + bX Please present the calculations and results and ANOVA

Graphs using a scatter diagram

Compute a moving average.

2. Determine a linear trend equation.

3. Compute a trend equation for a nonlinear trend.

4. Use a trend equation to forecast future time periods and to develop seasonally adjusted forecasts.

5. Make all possible observations and interpret the result

Prices Earning Billons

2.71 9.92

2.71 9.99

2.72 10

2.72 10.1

2.73 10.2

2.73 10.9

2.74 11.2

2.74 11.5

2.75 11.9

2.76 12.1

2.77 12.2

2.77 12.3

2.78 13.3

2.79 14.2

2.81 15.7

2.82 16.4

2.86 16.8

2.89 17.3

2.99 18.2

3.79 22

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Calculations are done in Excel.

1. I would like to a Use the regression equation: Y'= a + bX Please present the calculations and results and ANOVA

The general form of simple linear regression is Y= a + bX Where Y is the dependent variable and X is the independent variable. a and be are known as the regression coefficients .They are estimated by the method of least squares. The estimates of a and b are given by

,

The parameter b measures the impact of unit change in X on the dependent variable Y. It is the slope of the regression line. The parameter a is the value of Y when X=0. It is known as the Intercept term

The regression equation can be used to predict the value of Y for a given X. The predicted value of Y is given by

The correlation is given by the formula

The square of correlation between X and Y is known as the coefficient of determination (R2) . R2 gives the percentage of variation that can be predicated using the regression equation.

Time Prices: X Earning Billons ...

#### Solution Summary

This solution discusses regression and linear trend equations. Calculations for results and ANOVA are determined.