#$&* course Mth 152 7/21 10:40pm If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
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Given Solution: `aThe equation is obtained by substituting the weights for y and the heights for x in the formula for the regression line. You get y = 3.35 x - 78.4. To predict weight when height is 70 you plug x = 70 into the equation: y = 3.35 * 70 - 78.4. You get y = 156, so the predicted weight for a man 70 in tall is 156 lbs. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q Query problem 13.6.12 reading 83,76, 75, 85, 74, 90, 75, 78, 95, 80; IQ 120, 104, 98, 115, 87, 127, 90, 110, 134, 119 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: n=10, x-reading=811, y-IQ=1104, x^2=66225, y^2=124060, xy= 90437, 10(90437)-811(1104)/10(66225)-811^2=9026/4529=1.993, a=1.993. 1104-1.993/10=51.23, b= -51.23, 1.993x-51.23 is equation of regression line. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ 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 89 445 25 7921 15 417 1181 55 30,087 n=6, x=15, y=417, xy=1181, x^2=55, y^2=30,087, r= 6(1181)-15(417)/sq root of 6955)-(15^2)* sq. root of 6(30,087)-(417^2)= 831/sq. root of 105*5798= 831 sq. root of 608790= 831/780.2=1.065 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a **STUDENT SOLUTION: X Y XY X^2 Y^2 0 48 0 0 2304 1 59 59 1 3481 2 66 132 4 4356 3 75 225 9 5626 4 80 320 16 6400 5 90 450 25 8100 Sums= 15 418 1186 55 30266 The coefficient of the correlation: r = .996 I found the sums of the following: x = 15, y = 418, x*y = 1186, x^2 = 55 n = 6 because there are 6 pairs in the data I also had to find Ey^2 = 30266 I used the following formula: r = 6(1186) - 15(418) / sq.root of 6(55) - (15)^2 * sq. root of 6(30266) - (418)^2 = 846 / sq. root of 105 * 6872 = 846 / sq. root of 721560 = 846 / 849.4 = .996 ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I thought I had this correct, but looking at the solution where I got 417 you had 418, and you had 30,266 I had gotten 30,087. ------------------------------------------------ Self-critique Rating: 2 ********************************************* Question: `q Query problem 13.6.24 % in West, 1850-1990, .8% to 21.2% What population is predicted in the year 2010 based on the regression line? What is the equation of your regression line and how did you obtain it? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: n=8, x=56, x^2=560, y= 77.7, y^2 1110.43, xy=786.4 a=1.44, b= -.39, r=.99 2010 - x=16, y= 1.44(16-.39= 22.65 22.65% increase in population by year 2010. confidence rating #$&*: 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): ------------------------------------------------ Self-critique Rating: 3 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!