A. What is the expected price for a house with size 2000 square feet? Using relevant Excel output, discuss whether the margin of error of this expected price will be low or high. B. Using Excel, obtain the equation of the linear regression line that fits this data for price vs. number of bedrooms. Is the true slope different from zero? C. Which of these two variables – number of bedrooms or size, is the better predictor for price and why?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The sheet called HousePr contains data on prices of houses that have sold recently and two attributes of the house – the number of bedrooms and the size. Column 1 is the selling price of the house in thousands of dollars and column 2 is the size in hundreds of square feet.
A. What is the expected price for a house with size 2000 square feet? Using relevant Excel output, discuss whether the margin of error of this expected price will be low or high.
B. Using Excel, obtain the equation of the linear regression line that fits this data for price vs. number of bedrooms. Is the true slope different from zero?
C. Which of these two variables – number of bedrooms or size, is the better predictor for price and why?
Price SqrFoot Bedrooms
731 21 4
901 22 4
736 16 3
866 19 3
697 12 2
836 17 3
694 17 3
843 18 3
721 15 4
883 18 2
913 17 3
868 17 3
642 17 3
884 17 3
810 16 2
841 16 3
779 17 4
726 16 3
667 14 2
870 21 4
834 16 2
776 19 4
681 14 2
846 19 4
917 20 4
946 23 5
813 20 4
911 18 3
723 17 3
711 15 2
897 19 4
881 22 4
863 19 3
711 14 2
876 18 3
812 18 3
729 15 2
797 17 3
885 20 4
770 16 2
851 17 3
741 17 3
972 21 5
944 20 4
687 17 2
837 17 2
899 21 4
732 18 3
819 19 4
656 13 2
763 17 3
722 15 2
911 19 3
795 16 2
685 15 2
847 18 3
502 17 2
709 15 2
841 19 4
681 14 2
939 20 3
824 20 3
663 13 2
922 19 3
919 18 3
671 14 2
860 20 4
852 22 5
932 22 4
812 17 2
763 16 3
682 14 2
846 21 5
780 16 2
836 20 4
960 21 5
917 20 3
733 19 4
875 19 4
692 15 2
814 16 2
816 17 3
869 19 4
787 16 3
831 18 3
744 18 3
647 15 2
740 15 3
670 15 2
870 20 3
722 15 3
821 21 4
841 17 3
682 15 2
847 17 3
628 14 2
712 16 3
672 17 3
823 19 4
874 19 3
830 14 2
656 14 2
868 21 4
799 19 4
799 16 2
902 21 3
811 18 3
675 15 2
685 14 2
919 22 4
755 16 3
813 18 3
832 19 3
776 19 4
818 18 3
760 15 2
780 16 2
796 19 3
857 18 3
762 19 3
788 18 4
687 15 2
777 17 3
897 19 4
844 20 2
669 15 2
856 20 5
745 18 3
793 21 3
728 16 2
794 16 3
814 18 3
754 18 4
755 17 3
811 19 3
720 16 2
885 20 4
869 17 3
816 18 4
715 18 4
786 17 3
1034 25 5
823 17 2
748 17 3
891 21 4
771 14 2
792 17 4
768 16 2
1008 24 5
689 14 2
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