Notebook Tab 6 Pages 183 to 196 - Conte Solutions · 2015. 4. 13. · y b1x b0 e TOH in Linear...

Notebook Tab 6Pages 183 to 196

© 2014 ConteSolutions

When the assumed relationship best fits a straight line model (r (Pearson’s correlation coefficient) is close to |1|), this approach is known as Linear Regression Analysis.

Excel and Minitab gives r2 value

r is square root of r² with a + or - sign When the modeling analysis best fits a

straight line and includes only one independent variable, it is known as Simple Linear Regression Analysis.


ebxby 01

TOH in Linear Regression model (ANOVA) The null hypothesis (= sign) and a parameter

Null Hypothesis: All beta coefficients are equal to zero

Criteria - P-value from Minitab is less than P=0.05 we reject the null hypothesis

statistical significant alternative based on α = 0.05 Excel users note: 5.45E-05 is exponential notation

and equal to 0.0000545 (see Wikipedia)


Response variable and input variable Objective to predict dependent variable based on

the independent variable Example: predict customer satisfaction based on

wait time Strength of relationship is “Correlation Coefficient” The regression equation contains two values of

interest


baxy

Slope and intercept and error term Least squares method Least squares regression line Example: x is wait time, y is customer satisfaction

ebxby 01

HEIGHT WEIGHT70 15563 15072 18060 13566 15670 16874 17865 16062 13267 14565 139

The following data was collected to see if weight can be predicted from a person’s height:


Correlations: HEIGHT, WEIGHT R-Sq = 75.92%Square root of 0.7592 = 0.87

Pearson correlation of HEIGHT and WEIGHT = + 0.87Pearson Correlation Coefficients range between -1.0 and + 1.0They can be positive or negativeCustomer Satisfaction model it could be + or –

P-Value = 0.000477

H0: Slope and Intercept values = 0 (no linear correlation) (beta0 and beta1)

Ha: Slope and Intercept not = 0 (there appears to be a linear correlation)


Regression Analysis: WEIGHT versus HEIGHT

The regression equation is:

WEIGHT = - 62.8509 + 3.2553 x HEIGHT

Predictor Coef SE Coef T P

Constant -62.851 40.85 -1.54 0.158HEIGHT 3.2553 0.6455 6.28 0.000

Based on this analysis the independent variable, Height, does appear to be significant in predicting a person’s weight.


For this model,

S = 8.42 – the standard deviation of the distances the actual values are from the fitted line (smaller is better)

R-Sq = 75.92% - this model explains 75.92% of the variation in weights

Is the Model Statistically Useful?Model Diagnostics


H0: The model’s beta coefficients are all zero (none are useful in predicting the response variable

Ha: At least one of the model’s beta coefficients are not zero (at least one independent variable is useful in predicting the response variable)

What is your conclusion now?


A weak correlation coefficient does not mean that the model is not useful.

Remember that the correlation coefficient only tests for linear relationships and the relationship among the variables may be curvilinear.

A low R sq / R sq adj does not mean that the model is not useful.

It just means that is it not complete and that other terms need to be added to make it more effective at predicting the variation in the response variable.


Desktop Open Minitab File/Open Worksheet◦ Villanova/Correlation Exercise.XLS

Graph/Scatter Plot (with regression) Stat/Regression/Regression◦ Response=WEIGHT, Predictor=Height


Notebook Tab 6 Pages 183 to 196 - Conte Solutions · 2015. 4. 13. · y b1x b0 e TOH in Linear...

Documents

Transcript of Notebook Tab 6 Pages 183 to 196 - Conte Solutions · 2015. 4. 13. · y b1x b0 e TOH in Linear...