Are the number of bedrooms and number of bathrooms significant predictors of monthly rent in the multiple regression model we estimated in class? Jill Student Westminster College Salt Lake City, UT Sophomore Economics Spring 2015 semester April 25, 2015

Descriptive Statistics

Simple Regression 1 H 0 :   1 = 0 H a :   1 0 y =   0 +   1 · x 1 +  I estimated the following simple regression model The coefficient significance test for number of bedrooms: where y= monthly rent x 1 =number of bedrooms   1 =the variable’s coefficient that cannot be know, but can be estimated  =the errors that cannot be known, but can be estimated

R 2 implies what? T-test implies what? F-test implies what? Simple Regression 1

H 0 :   2 = 0 H a :   2 0 y =   0 +   2 · x 2 +  I estimated the following simple regression model where y= monthly rent x 2 =number of bathrooms   2 =the variable’s coefficient that cannot be know, but can be estimated  =the errors that cannot be known, but can be estimated Simple Regression 2 The coefficient significance test for number of bathrooms:

Simple Regression 2 R 2 implies what? T-test implies what? F-test implies what?

H 0 :   1 = 0 H a :   1 0 y =  0 +  1 · x 1 +  2 · x 2 + ···  +  35 · x 35 +  In class, we estimated the following regression model where y= monthly rent x=the independent variables (number of bedrooms, number of bathrooms…)   =the parameters that cannot be know, but can be estimated  =the errors that cannot be known, but can be estimated There are 35 individual significance tests, one for each variable in our multiple regression I test for coefficient significance test for number of bedrooms and number of bathrooms: Multiple Regression coefficient significance t tests H 0 :   2 = 0 H a :   2 0

Multiple Regression coefficient significance

Multiple Regression coefficient significance

H 0 :   1 =   2 = … =   35 = 0 y =  0 +  1 · x 1 +  2 · x 2 + ···  +  35 · x 35 +  In class, we estimated the following regression model where y= monthly rent x=the independent variables (number of bedrooms, number of bathrooms…)   =the parameters that cannot be know, but can be estimated  =the errors that cannot be known, but can be estimated There is one model significance test: Multiple Regression model significance F test H a :   1 =   2 = … =   35 0

Multiple Regression model significance

The F test in the multiple regression … The adjusted R 2 in the multiple regression … The number of bedrooms is a(n) (in)significant predictor of monthly rent Its coefficient implies … The number of bathrooms is a(n) (in)significant predictor of monthly rent Its coefficient implies … Conclusions