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Exam Formula on Applied Business and Economics Statistics II | ECON 309, Exams of Economics

California State University (CSU) - Los Angeles Economics

Prof. Nikolai Pulchritudoff

all exam fomula Material Type: Exam; Professor: Pulchritudoff; Class: APPLIED BUSINESS AND ECONOMIC STATISTICS II; Subject: Economics; University: California State University - Los Angeles; Term: Summer 2011;

Typology: Exams

2010/2011

Uploaded on 09/29/2011

opc-02 🇺🇸

2 documents

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x 12 21 28 8 20

y 17 15 22 19 24

x y x2 xy

140 25 19600 3500

119 29 14161 3451

103 46 10609 4738

91 70 8281 6370

65 88 4225 5720

29 112 841 3248

24 128 576 3072

571 498 58293 30099 0.5545917

404.91667

SSxy 30099-((571*498)/7) -10523.57

SSxx 58293-((571^2)/7) 11715.71

b1 -0.898247 15.2270607071

b0 ((498/7)-(-0.89825)(571/7) 144.4144

y^=144.4144-0.898x

47.6 15.1 2265.76 228.01 718.76 Ssxy 12.046667

47 15.1 2209 228.01 709.7 SSxx 45.733333

50.6 16 2560.36 256 809.6 b1 0.263

52.6 15.6 2766.76 243.36 820.56 b0 2.301

54.4 16.4 2959.36 268.96 892.16

53 18.3 2809 334.89 969.9 550.934222222

g21/g22 213.8853403

305.2 96.5 15570.24 1559.23 4920.68 Ssxy/SSxx 0.79113539365

1 47.6 15.1 2265.76 228.01 718.76

2 47.3 15.4 2237.29 237.16 728.42

3 50.6 15.9 2560.36 252.81 804.54 10.146667

4 52.6 15.6 2766.76 243.36 820.56 32.41333 7.1533333 231.863377778

5 52.4 16.4 2745.76 268.96 859.36 0.66635753688

6 52.9 18.4 2798.41 338.56 973.36

303.4 96.8 15374.34 1568.86 4905

x y y^ (y-Y^)

0.05153 12 17 18.4582 -1.4582 2.126347

0.00292 21 15 19.9196 -4.9196 24.20246

0.01513 28 22 21.0563 0.9437 0.89057

0.04326 8 19 17.8087 1.1913 1.419196 0.6

0.00372 20 24 19.7572 4.2428 18.00135 3.9429231

0.07952 0 46.63993 15.54664

0.02465

Partial preview of the text

Download Exam Formula on Applied Business and Economics Statistics II | ECON 309 and more Exams Economics in PDF only on Docsity!

x 12 21 28 8 20 y 17 15 22 19 24 x y x2 xy 140 25 19600 3500 119 29 14161 3451 103 46 10609 4738 91 70 8281 6370 65 88 4225 5720 29 112 841 3248 24 128 576 3072 571 498 58293 30099 0.

SSxy 30099-((571*498)/7) -10523. SSxx 58293-((571^2)/7) 11715. b1 -0.898247 15. b0 ((498/7)-(-0.89825)(571/7) 144. y^=144.4144-0.898x 47.6 15.1 2265.76 228.01 718.76 Ssxy 12. 47 15.1 2209 228.01 709.7 SSxx 45. 50.6 16 2560.36 256 809.6 b1 0. 52.6 15.6 2766.76 243.36 820.56 b0 2. 54.4 16.4 2959.36 268.96 892. 53 18.3 2809 334.89 969.9 550. g21/g22 213. 305.2 96.5 15570.24 1559.23 4920.68 Ssxy/SSxx 0. 1 47.6 15.1 2265.76 228.01 718. 2 47.3 15.4 2237.29 237.16 728. 3 50.6 15.9 2560.36 252.81 804.54 10. 4 52.6 15.6 2766.76 243.36 820.56 32.41333 7.1533333 231. 5 52.4 16.4 2745.76 268.96 859.36 0. 6 52.9 18.4 2798.41 338.56 973. 303.4 96.8 15374.34 1568.86 4905 x y y^ (y-Y^) 0.05153 12 17 18.4582 -1.4582 2. 0.00292 21 15 19.9196 -4.9196 24. 0.01513 28 22 21.0563 0.9437 0. 0.04326 8 19 17.8087 1.1913 1.419196 0. 0.00372 20 24 19.7572 4.2428 18.00135 3. 0.07952 0 46.63993 15.

- 0.02789
  - 0.0016
- 0.02074 -
- 0.04162

0.001764 -0.
0.314344 140.

ŷ=β0+β1x B1=slope x y X^ 1 140 25 19600 1 119 29 14161 1 103 56 10609 14.40127 1 91 70 8281 2016.432 1 50 88 2500 3037.41 1 29 117 841 15852.19 1 24 128 576 203.8156 7 556 513 56568

41041.41 47.6 15. 70969.21 -46.29 15.24 47.3 15. 108.7575 50.6 15. 52.6 15. x y y2 xy 52.4 16. 139 24 576 3336 52.9 18. 122 28 784 3416 106 47 2209 4982 94 73 5329 6862 68 85 7225 5780 28 115 13225 3220 24 129 16641 3096 581 501 45989 30692 SSE -

XY

3500 SSxy -10792. 3451 SSxx 12405. 5768 b1 -0. 6370 b0 142. 4400 3393 3072 29954 r

SUMMARY OUTPUT

Regression Statistics Multiple R 0. R Square 0. Adjusted R 0. Standard E 10. Observatio 7 ANOVA df SS MS F Significance F Regression 1 11376.01 11376.01 110.2966 0. Residual 5 515.7008 103. Total 6 11891. CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 99.0%Upper 99.0% Intercept 156.8881 8.134167 19.28754 6.91E-06 135.9785 177.7976 124.0899 189. X Variable -1.06724 0.10162 -10.50222 0.000135 -1.328463 -0.806016 -1.476988 -0.

66 90 find t 29 109 Regression 23 130

ep round or don't round he number in the cell to the left formulas in each cell. F41. Check the formula in G41. rounded numbers. hich exist ONLY in columns G and K. G41 and K35. m using. You can also press at once. Press "Ctrl" and "~" again the t Table to get ed there for TINV(ALPHA,n-k-1), d I gone to the table. value: a=0.01 a/2=0. a= 1- 99% confidence interval interest rate of 9% b1 = -0.617329 -0. bo = 14.46209 14. SSE = 16.97473 16. Se = 2.378706 2. Xo-Xbar 0.8 0. (Xo-Xbar)^2 = 0.64 0. ((Xo-Xbar)^2 )/ SSxx = 0.005776 0. 1/n = 0.2 0. SQRT((1/n) + ((Xo-Xbar)^2 )/ SSxx) = 0.453626 0. t(ALPHA/2,5) Se = 13.89574 13. SA = t(ALPHA/2,5) Se SQRT = 6.303463 6. Upper Limit = 15.212 15. Lower Limit = 2.606 2. have trouble where I used rounded numbers*

For 90% Prediction Interval with Xo = 100:

th x = 100: 38.520 ≤ y ≤ 71.

Solution to Q13 Part A (Xo = 100) L

Try doing Part B (Xo = 130), using my procedure; at every step round or don't round because of rounding. Notice that in the cells with pink baground I have rounded the number in the cell to the left to 3 decimals. So, pay attention when I use pink cells & when I don't in the formulas in each cell. For example,in G41 I rounded to 3 digits the number in cell F41. Check the formula in G41. When studying the formulas in the cell, it is easy when I use rounded numbers. because the rounded numbers appear ONLY in pink cells, which exist ONLY in columns G and to calculate, e.g. in cell J41 I used the "rounded" pink cells G41 and K35. Click on the cell J41 to see in the fx window the formula I am using. You can also press simultaneusly "Ctrl" and "~" to see ALL formulas in all cells at once. Press "Ctrl" and "~" ag to go away from formulas & back to numbers. Check how in cell F41 I used a formula rather than going to the t Table to get the needed t value. Had I gone to the table I would have looked there for t(ALPHA/2, n-k-1), however, in the formula I had to type in = TINV(ALPHA,n-k-1), so that I used 0.10 instead of 0.05 that I would have used had I gone to the table. x y x^2 xy 1 (^140 25) 19600 3500 1 (^119 29) 14161 3451 1 (^103 47) 10609 4841 1 (^91 70) 8281 6370 1 (^66 88) 4356 5808 1 (^29 111) 841 3219 1 24 128 576 3072 SUMS 7 572 498 58424 30261 AVERAGES 81.7143 71.1428571429 8346.285714286 4323 SSxy = -10432. SSxx = 11683. Xo1 = 100 54.81 54. ALPHA/2 = 0. n = 7 df = n-2 = 5 t(ALPHA/2,5) = 2.015048372088 2. My answers in cells wi tan background Answers in WileyPlus in cells with gray background exactly when I did or did not. I suspect that many of you will have trouble To make it even more easy, the numbers in red are in cells where I used rounded numbers Yhat( 100 ) = 90% prediction interval for a single value of y with x = 100: 38.520 ≤ y ≤ 71.