Linear Regression

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TThis is the modeling of a conditional relation as a straight line between two variables. Y is often dependent on X; hence, regression is used for modeling Y behavior in X, as it was in the prediction, outside of the established data set.
How do I regress linearly in SPSS? he data that is to be analyzed need to satisfy some assumptions. These assumptions are:
• The two variables should be measured at the continuous level
• The observations should be independent.
• No conspicuous outliers.
• Data needs to show homoscedasticity.
i. You first click on Analyze which is on the top menu, then Regression and then Linear.
ii A new linear Regression dialogue box will pop up. In the dialogue box, the left side has variables which you should distinguish if they are either dependent or independent. Transfer the dependent and independent variables into their respective slots by either drag-and-dropping the variables or using the transfer buttons.
iii. The final step requires the analyzer to click the okay button for it to generate the results.
What is the equivalent to R2 in simple linear regression?
In Simple Linear Regression, the equivalent of the coefficient of determination (R2) is the square of the sample coefficient of correlation denoted as r2.

Provide an example where the outlier is more important to the research than the other observations?
Outliers are extreme observations that are as important as other observations in research.
Suppose it has been decided that only those students who will get a scholarship in a class of 100 students are those who score exceptionally well on a test as compared to others. So we plot the test-scores of the students and observe if any of those scores are above Q3 + 1.5 IQR, where Q3 is the third quartile and IQR = Interquartile range = Q3 – Q1. So here we are more interested in the observations which are outliers than the normal observations.

When is R2 more useful than R in linear regression?
R2 is more useful than R in linear regression when one needs to explain the proportion of total variance of the y variable predicted by x variable. When there is more than one explanatory variable to be tested.

References
Seber, G. A. F., & Lee, A. J. (2012). Linear Regression Analysis. Hoboken: Wiley.

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