#$&* course Mth 152 1158 pm 73113 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
.............................................
Given Solution: `aThe equation is obtained by substituting the weights for y and the heights for x in the formula for the regression line. You get y = 3.35 x - 78.4. To predict weight when height is 70 you plug x = 70 into the equation: y = 3.35 * 70 - 78.4. You get y = 156, so the predicted weight for a man 70 in tall is 156 lbs. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Ok! ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q Query problem 13.6.12 reading 83,76, 75, 85, 74, 90, 75, 78, 95, 80; IQ 120, 104, 98, 115, 87, 127, 90, 110, 134, 119 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 83 120 9960 6889 76 104 7904 5776 75 98 7350 5625 85 115 9775 7225 74 87 6438 5476 90 127 11430 8100 75 90 6750 5625 78 110 8580 6084 95 134 12730 9025 80 119 9520 6400 811 1104 90437 66225 10(90437)-811(1104)/10(66225)-811^2 904370-895344/662250-657721 9026/4529 a=1.99 1104-1.99*811/10 1104-1613.89/10 b=-50.989 y’=1.99x-50.989 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
.............................................
Given Solution: `a n = 10 sum x = 811 sum x ^2 = 66225 sum y = 1104 sum y^2 = 124060 sum xy = 90437 a = [10(90437) - (811)(1104)] / [10(66225) - (811^2)] = 1.993 a = 1.99 b = [1104 - (1.993)(811) / 10 = -51.23 y' = 1.993x - 51.23 is the eqation of the regression line. ** STUDENT QUESTION How did you get sum x ^2 = 66225??? Is it not 811 * 811 = 657721? How did you come up with sum y^2 = 124060??? Is it not 1104 * 1104 = 1218816? I worked it out, can you tell me where I went wrong??? And I will try to rework the problem. INSTRUCTOR RESPONSE You didn't distinguish between sum x^2 and (sum x)^2. Sum x^2 means you figure out x^2 for every value of x, then add them. Remember that exponentiation precedes addition. (sum x)^2 means you add all the x values then square them. The same comment applies to sum y^2 vs. (sum y)^2. You didn't ask, but sum xy can also be confusing: • Sum xy means multiply each x value by the corresponding y value, then add the products. This is order of operations: multiplication before addition &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q Query problem 13.6.15 years 0-5, sales 48, 59, 66, 75, 80, 89 What is the coefficient of correlation and how did you obtain it? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 0 48 0 0 2304 1 59 59 1 3481 2 66 132 4 4356 3 75 225 9 5625 4 80 320 16 6400 5 90 450 25 8100 15 418 1186 55 30266 R=6*1186-6270/sqrt6*55-15^2*sqrt6*30266-418^2 846/sqrt] 330-225*sqrt181596-174724 846/sqrt721560 846/849 R=.996 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
.............................................
Given Solution: `a **STUDENT SOLUTION: X Y XY X^2 Y^2 0 48 0 0 2304 1 59 59 1 3481 2 66 132 4 4356 3 75 225 9 5626 4 80 320 16 6400 5 90 450 25 8100 Sums= 15 418 1186 55 30266 The coefficient of the correlation: r = .996 I found the sums of the following: x = 15, y = 418, x*y = 1186, x^2 = 55 n = 6 because there are 6 pairs in the data I also had to find Ey^2 = 30266 I used the following formula: r = 6(1186) - 15(418) / sq.root of 6(55) - (15)^2 * sq. root of 6(30266) - (418)^2 = 846 / sq. root of 105 * 6872 = 846 / sq. root of 721560 = 846 / 849.4 = .996 ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `q Query problem 13.6.24 % in West, 1850-1990, .8% to 21.2% What population is predicted in the year 2010 based on the regression line? What is the equation of your regression line and how did you obtain it? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 0 0.8 0 0 0.64 2 2.6 5.2 4 6.76 4 5.0 20.0 16 25.0 6 7.7 46.2 36 59.29 8 10.0 80.0 64 100.0 10 13.3 133.0 100 176.89 12 17.1 205.2 144 292.41 14 21.2 296.8 196 449.44 56 77.7 786.4 560 1110.43 A=8(786.4)-56(77.7)/8(560)-56^2 6291.2-4351.2/4480-3136 1940/1344 A=1.44 77.7-1.44*56/8 77.7-80.64/8 b=-0.3675 Y’=1.44*16-0.3675 Y’=22.67 R=8(786.4)-56*77.7/sqrt8(560)-(56^2)*sqrt8*1110.43-(77.7^2) 6291.2-4351.2/4480-3136*8883.44-6037.29 1940/37*53 1940/1961 R=.989 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
.............................................
Given Solution: `aSTUDENT SOLUTION: Calculating sums and regression line: n = 8 sum x = 56 sum x^2 = 560 sum = 77.7 sum y^2 = 1110.43 sum xy = 786.4 a = 1.44 b = -.39 r = .99 In the year 2010 the x value will be 16. y' = 1.44(16) - .39 = 22.65. There is an expected 22.65% increase in population by the year 2010. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!