Question

Value Rental Value Rental Value Rental Value 810006656 770004576 75000 7280 67500 95000 7904 94000 8736 90000 6240 85000 12100012064 115000 7904 110000 7072 104000 135000 8320 130000 9776 126000 6240 125000 145000 8320 140000 9568 140000 9152 135000 16500013312 165000 8528 155000 | 7488 148000 17800011856 174000 10400 170000 9568 170000 20000012272 200000 10608 194000 11232 190000 214000 8528208000 10400 200000 10400 200000 240000 10192 240000 12064240000 11648 225000 28900011648 270000 12896 26200010192 244500 325000 12480 310000 12480 30300012272 300000 Table 1: Data of House Value versus Rental Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 12480

Answer 1

(a) Both the column (Value, Rental) is normally distributed. So we calculated the Pearson correlation coefficient. Our null hypothesis was there is no correlation between the variables( Value, Rental). And the alternative hypothesis was there is a correlation between both variables(Value, Rental). From the calculation, we got the p-value 0.000 which is less than 0.05. Therefore we reject the null hypothesis. That is we got there is a correlation between the variables. The Pearson correlation coefficient value is 0.765.

(b) We did the linear regression analysis. That is Rental=a+ b* Value. From this, we got the standard error of the estimate is 0.003.

(c) From the above regression analysis, we have got the linear equation Rental= 5363.87+ 0.024*Value. The predicted value for the $230000 is 10883.87. 95% of the prediction interval for the rental income on a house for $230000 is  (9191.29, 12576.45).