An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments,based on the size of the apartment,as defined by square footage.A sample of eight apartments in a neighborhood was selected,and the information gathered revealed the data shown below.For these data,the regression coefficients are bo=373.5333 and b1=0.8553.Complete parts(a)through(d). Monthly Rent($); 9001,500,800,1600,1950,925,1825,1400, Size(Square Feet);850,1300,1050,1100,2000,650,1350,950 a.Determine the coefficient of determination, and interpret its (Round to three decimal places as needed.)

To determine the coefficient of determination (R^2), we first need to calculate the predicted values of the monthly rent using the given regression coefficients (bo and b1) and the size of the apartments.

The regression equation is: Y = bo + b1*X where Y is the dependent variable (monthly rent), X is the independent variable (size of the apartment), bo is the y-intercept, and b1 is the slope of the regression line.

Using the given regression coefficients, the equation becomes: Y = 373.5333 + 0.8553*X

Now, we substitute the size of each apartment into the equation to get the predicted values of the monthly rent.

After calculating the predicted values, we calculate the total sum of squares (SST), the regression sum of squares (SSR), and the error sum of squares (SSE).

SST is the total variation in the dependent variable (monthly rent). It is calculated as the sum of the squared differences between the actual values of the dependent variable and its mean.

SSR is the variation in the dependent variable explained by the independent variable (size of the apartment). It is calculated as the sum of the squared differences between the predicted values of the dependent variable and its mean.

SSE is the variation in the dependent variable not explained by the independent variable. It is calculated as the sum of the squared differences between the actual values and the predicted values of the dependent variable.

Finally, the coefficient of determination (R^2) is calculated as: R^2 = SSR/SST

R^2 is a measure of how well the regression line fits the data. It ranges from 0 to 1. A value of 1 means that the regression line perfectly fits the data, while a value of 0 means that there is no linear relationship between the independent and dependent variables.

To interpret R^2, we say that it is the proportion of the variation in the dependent variable that is explained by the independent variable. For example, if R^2 is 0.85, we can say that 85% of the variation in the monthly rent is explained by the size of the apartment.