How Is Multiple Regression Different from Simple Linear Regression - Assignment Example

For any fixed value of x, the response variable y varies normally around this mean and has a standard deviation σ that is the same for all values of x.
Multiple regression extends simple linear regression to include several explanatory variables (or predictors). Everything we learned about simple linear regression is a special case of multiple regression. Multiple regression is required when a single-predictor model is inadequate to describe the true relationship between the response variable y and its potential predictors (x1, x2, x3 . . .). Adding predictors is more than a matter of “improving the fit.”

Multiple regression is used to define a linear relationship between a response variable y and more than one explanatory variable x. In multiple regression, more than one explanatory variable is used to explain or predict a single response variable. The multiple regression model assumes that the mean of the response variable y depends on p explanatory variables according to a linear function ‘μy = β0 + β1x1 + β1x2 +…+ β1xp’. In this case, the mean response is not observed, as the observed values of y vary about their means. However, we can think of subpopulations of responses, each corresponding to a particular set of values for all of the explanatory variables, and in each subpopulation, y varies normally with a mean given by the population regression equation. The regression model assumes that the standard deviation σ of the responses is the same in all subpopulations.

M9 Logistic Regression Discussion
Define logistic regression. Explain the difference between linear and logistic regression.
A logistic regression is used when the response variable has only two possible values such as success or failure, live or die, acceptable or not. Logistic regressions work with odds rather than proportions. The odds are simply the ratio of the proportions for the two possible outcomes. The logistic regression model relates the log of the odds to the explanatory variable. A logistic regression models the log odds as a linear function of the explanatory variable, which is given by the equation ‘log odds = β0 + β1x’.
Simple linear regression is a flexible way of analyzing linear relationships between two quantitative variables. A key assumption for a simple linear regression model is that the deviations from the model fit are normally distributed.

The response variable distribution is given by the binomial distribution.

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