postillan4

2021-02-10

Suppose x1 and x2 are predictor variables for a response variable y.
a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable.
b. State the four assumptions for multiple linear regression inferences

lamanocornudaW

Step 1
a.
Yes, the distribution of the response or dependent variable is the distribution of all the possible values of the dependent variable corresponding to particular values of two predictor or independent variables.
Although, the assumptions are not actually about only the distribution of the dependent variable, it is about the distribution of y for given x1 and x2.
Step 2
b.
The four assumptions for multiple linear regression inferences are as follows:
Linearity: There must be linear relationship between the independent and the dependent variables which can be tested with the help of scatterplots.
Normality: The multiple linear regression assumes that the residuals are normally distributed, that is, the errors between the values of predictor and the response variables. It can be checked by looking at a histogram or a Q-Q-Plot.
Multicollinearity: It is assumed by the multiple regression that the predictor variables are not highly correlated with each other. It can be tested using correlation matrix or variance inflation factor (VIF). The data should be centered if multicollinearity is found in the data.
Homoscedasticity: According to this assumption, the variance of the error terms is similar across the values of the predictor variables. The cone shaped pattern observed by the scatterplot between residuals and predicted values shows the heteroscedasticity in the data.

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