Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES=a+BAGE+YMIL+&ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predictor 1.7586 0.2124 Constant 0.2525 6.9648 0.0000 0.3175 0.3586 AGE 0.5042 MIL -0.7527 -2.0991 ** ENG 4.8124 0.6196 7.7664 0.0000 R-sq=56.1% R-sq (adj) =59.8% Analysis of Variance Source DF MS F Regression 3 413.1291 138.7097 0.00 *** Error 50 457.7607 2.2888 Total 53
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values ‘*’, ‘**’, ‘***’and ‘*****’.
d) Hence test whether ? is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis.
f) Given an interpretation of the term “R-sq” and comment on its value.
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