Question

Concept Questions

1. We've discussed that a linear regression assumes the relationship between variables is linear: it forms a constant slope. But suppose the data is U-shaped or inverted U-shaped. How would you created a linear regression so the line would follow this data? (hint: think of what the equation for a U-shaped line looks like.)
2. Suppose you applied a scalar to a variable. Then you used both the original variable and the scaled variable as explanatory variables. What would happen and why?

Answer 1

suppose the data is U-shaped then realation ship is

y=X^2

hence instead of having equation y=a+b*x

we create linear regression using equation

y=a+b*x^2

If you used both the original variable and the scaled variable then the problems that can be encountered using these variables is the problem of multicollinearity,
ie. two or more factors amongst this list of factors might be coorelated which can give us flawed results.
Here original variable and the scaled variable might be coorelated.