Answers
(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).
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