Regression

Regression
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Question One
Correlation is a measure of fluctuation between two or more variables together and can either be positive or negative. On the other hand, causality is a cause-effect phenomenon where the measure of one event decreases or increases due to the introduction or application of another or other events. Correlation is a relationship whereas causality is a cause-and-effect. For instance, a correlation may appear between drug abuse and crime, in that both occur in high or low levels in the same population. It is however statistically invalid to presume that drug abuse causes crime or that crime causes drug abuse without investigating the effect of another variable or variables (Triola, 2006).
Question Two
Y = Β0 + Β1X is a population parameter whose values of B0 (a constant) and B1 (the regression coefficient of X) are estimated by use of the sample statistic regression equation ŷ = b0 + b1x. Y indicates the value of the outcome variable whereas ŷ indicates the estimated value of the outcome variable. It, therefore, follows that Y is a fixed, unknown population characteristic that can only be estimated using ŷ, a known characteristic of the sample (Triola, 2006).
Question Three
The geneticist can use a nonlinear regression model. The nonlinear model is more flexible in the types and shapes of curves it can fit appropriately. It is however important for the geneticist to use a linear regression model first and evaluate whether the resulting fit adequately represents the data.

The geneticist can do this by creating a residual plot and check for random residuals. Any non-random patterns in the residuals will indicate that the linear model fails to represent the data adequately, and therefore the need to use nonlinear regression (Triola, 2006).
References
Triola, M. F. (2006). Elementary statistics. Reading, MA: Pearson/Addison-Wesley.