Question

Problem 1 Please do not use any type of software to solve this problem; perform all the calculations and draw the charts by hand. You can use your calculator only for simple operations like addition, multiplication, finding averages and standard deviations. The owner of an apartment complex with three-bedroom units is trying to determine what rent he should set for the summer months. He believes that the rent of an apartment in his complex determines if it will be occupied during the summer. To test this theory, he collected data from 10 other apartment complexes with similar three-bedroom units in close proximity to his neighborhood: Units occupied Rent ($) 1500 1600 2000 1100 1050 1750 1300 1250 1850 1900 (a) Develop a scatter plot for these data. Does a linear relationship appear reasonable? Explain. (Be careful when redrawing the axes and creating the scatterplot in your homework by hand. The axes cross at (1000, 35).) Units occupied 1000 1200 1400 1600 1800 2000 Rent

Answer 1

For your data, the regression equation for Yis: y = -0.01068X + 60.93827 As you can see the output from this calculator is fairly verbose. Mostly it should be self- explanatory, but you should note that any apparent discrepancies in calculations are because rounding is used for the purposes of display, but not for the calculations themselves. If you wish to perform a further calculation, it is necessary to hit the reset button at the bottom of the page Y Values X Values 1500 1600 2000 1100 1050 1750 1300 1250 1850 Y. Dependent 1900 M: 1530 M:44.6 1000 1300 1900 2200 1600 X-Independent Regression Linely--0.01% 60.94 Estimate Calculation Summary Sum of X= 15300 Sum of Y = 446 Mean X= 1530 Mean Y = 44.6 Sum of squares (55%) = 1061000 Sum of products (SP) = -11330 Regression Equation =ý=bX+ a b= SPISSX=-11330/1061000 = -0.01068 a = My-bMy = 44.6-(-0.01*1530) = 60.93827 = -0.01068X + 60.93827 X-Mx Y-My (X-M.)2 (X-MXXY-My) -1.6 -430 -480 900 4900 220900 184000 230400 48400 52900 78400 102400 136000 -4042 - 1892 3072 -1012 220 230 -280 -952 1728 320 370 2072 SS: 1061000 SP: -11330

Y Values X Values 1500 1600 2000 1100 1050 1750 1300 1850 1900 X-M, (Y-M 30 000 70.000 000 130.000 ER DOO 100 0.400 -8.800 4.400 6.400 00 000 220900.000 184000000 230400.000 400 000 52900 000 78400.000 1024400 000 138900.000 2500 0.160 73.900 12.360 40.960 21.100 0.160 11.50 20.160 31.350 (X-MXY-M 48 000 2010 4062000 102 000 3072 000 -1012 000 92.000 952.000 1728.000 2072.000 200 000 32000 370.000 2.400 5.400 -5.600 ME1530.000 My: 44.600 Sum: 1061000.000 Sum: 230 400 Sum-11330.000 Result Details & Calculation Key X Values - 15300 Mean - 1530 (X-M) 255-1061000 XX Values Y Y Values My Mean of X Values Mji Mean of Y Values X-Me & Y - My Deviation scores X-M) & (Y-My Deviation Squared X-MXY - My Product of Deviation Scores Y Values -446 Mean 446 (Y. My) 255y. 230.4 X and Y Combined N=10 50 - MMY - MB) = -11330 R Calculation r20%.MXY.M.)/VISS, 55 r.11330 / VI(1061000X230,4)) -0.7247 Meta Numerics (cross-check) -0.7247 The value of Ris -0.7247. This is a moderate negative correlation, which means there is a tendency for high X variable scores to go with low Y variable scores (and vice versa). The value of R, the coefficient of determination, is 0.5252.
B)rent variable

mean=1530

Sd=343.3

Unit. Occupied variable

mean=44.6

SD=5.06

C) correlation. -0.72

ans :I attached image

D),E) and F) also attached image

G) regression equations is

y=60.938 -0.0107X

X=1900

y=60.934+20.273

y=81.207

I )coefficient of determination 0.5252

I attached image correlation image (Last line)