# Linear Regression

**Topics:**Normal distribution, Regression analysis, Polynomial

**Pages:**3 (525 words)

**Published:**April 20, 2014

A. DETERMINE IF BLOOD FLOW CAN PREDICT ARTIRIAL OXYGEN.

1. Always start with scatter plot to see if the data is linear (i.e. if the relationship between y and x is linear). Next perform residual analysis and test for violation of assumptions. (Let y = arterial oxygen and x = blood flow). twoway (scatter y x) (lfit y x)

regress y x

rvpplot x

2. Since regression diagnostics failed, we transform our data. Ratio transformation was used to generate the dependent variable and reciprocal transformation was used to generate the independent variable.

3. Check if the model is adequate by checking the t-statistic, R2 and F-statistic. F statistic reveals that the equation used to determine the relationship between the x and y is functional. Using the test statistic for the test of coefficients, it was revealed that the constant value in the equation is not significantly different from 0. Also, it was revealed that the transformed x, significantly explains the dependent variable. Also, it was revealed that the measure of proportion of variability explained by the fitted value is relatively high with 96.23%. This means that transformed data in blood flow explains 96.23% of the variation in the transformed data in arterial oxygen. 4. Check the normality of residuals and equal variances

predict r, resid

kdensity r, normal

pnorm tx

qnorm tx

rvpplot tx

Before we could perform the numerical test, we must first generate the r by the command “predict r, resid” swilk r

5. Check the homoscedasticity of the residuals by using

rvfplot, yline(0)

Further check assumption by using the numeric tests:

6. CONCLUSION: I may conclude that the best model fitted on the data is and that the model is adequate. Also, the assumptions of normality and equal variances were met.

B. DETERMINE THE STOPPING DISTNCE AT VARIOUS SPEEDS.

1. Determine the scatter plot first to check normality. (Let y = stopping distance and x = speed). twoway (scatter y x)...

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