Imagine you were hired by a large corporation to investigate whether there exists a relationship between the number of days an employee works from home every year and the distance between the employee's home and the office.

A sample of 50 employees was selected for the analysis and you found a linear pattern in the scatterplot of the data. You performed a simple linear regression, taking 'number of days an employee works from home' as the dependent variable and 'distance between the employee's home and office' as the independent variable.

This analysis aimed to determine whether employees living far from the office availed more work from home days than the others.

The output from the Excel tool is shown in the table given below:

PredictorCoefficientStd Errt-Valuep-ValueConstant8.0978

0.808810.01190.0003Distance to Office-0.34420.0776-4.43480.0022

R-squared = 0.7109

Formulate the null and alternative hypotheses for simple linear regression?