Question

The sidereal year of a planet is related to the distance of the planet from its sun through a power equation. The following data for a distant solar system show the distances its planets are from their sun and the planets' sidereal years. Complete parts (a) through (d). Distance from sun, x (Millions of miles) 40 Sidereal Year, y 0.29 109 1.27 187 2.84 791 24.39 1822 84.56 2567 140.93 3367 211.15 (a) Draw a scatter diagram treating distance from the sun as the explanatory variable. Select the graph below that resembles your scatter diagram. O B. O A. AY Ay 200- 200- 100- 100 X 0- 0 4000 4000 0 D. C. Ay 200- 200- 100- 100 X 0- 0 4000 4000 (b) Determine the logarithm of both the x- and y-values so that X log x and Y log y. Draw a scatter diagram of the transformed data. Enter the log values in the table below. Round each value to four decimal places. Y log y X =log x y X 0.29 40 (b) Deternine the logarithm of both the x- and y-values so that X= log x and Y log y. Draw a scatter diagram of the transformed data. Enter the log values in the table below. Round each value to four decimal places. Y log y X log x y 0.29 40 1.27 109 2.84 187 791 24.39 1822 84.56 2567 140.93 211.15 3367 Select the graph below that resembles your scatter diagram. O A. O B. AY=log y AY log y 2 1- 1 0- 3 4 2 4 X- log x x log x O D O C. V-In ? Select the graph below that resembles your scatter diagram. O B. O A. AY log y AY log y 2- 2- 1- 0- 3 2 -1- X log x X log x O C. O D. AY log y AY log y 2- 2 1 X log x X log x (c) Find the least-squares regresson line of the transformed data. Y = D-x-A (Do not round until the final answer. Then round to four decimal places as needed.) (d) Find the power equation of best fit. N y = ?

Answer 1

Bock1 Micrasaft Excel Home Insert Page Layoin Famulas Data Review VIEW AutaSum Bad Wrap Text General A Caibri 11 Normal Goud FII Copy Calculation Check Cell Sort &Find &6 Concitional Fermat as Neutral Formatting Table Insert Delete Forma Merge & Center Paste m B A Fcrmst Painter Clear Fiter Select Number clipbeard Alignment Fonm Styles Cels Edting R12 P Q E 5 T A C D G H K M N O R U Ve 1 x 40 2 0.29 1.27 3 109 2.84 4. 187 250 g4 56 1822 7 2567 140.93 211.15 3367 200 11 150 12 13 Series1 14 100 17 50 18 19 0 500 1000 1500 2000 2500 3000 3500 4000 22 23 24 27 28 29 30 Sheet1 Sheet2 Sheet3 100% Reacy 658 AM Type here to search G a201g

Bock1 Micrasaft Excel Нсm Insert Page Layoin Famulas Data REvew VIEW Cit AutaSum Bad Caibri Wrap Text General 11 A Normal Goud FII Copy Calculation Concitionsl Fermat as Neutral Formatting Table Sort &Find & Irsert Delete Forma Merge & Center Check Cell Paste A B Format Paintor Clear Fiter Select clipbeard Alignment Number Fom Styles Cels Edting 830 F F K R S P A G M N C T log x log y 1 2 40 1.6021 0.29 0.5376 3. 109 2.0374 1 27 .1038 4. 187 2.2718 2.8 0.4533 3 2605 1822 1 9772 7 2567 3.4094 140.93 2.1490 2.3246 3367 3.5272 211.15 9 SUMMARY OUTPUT 2.5000 11 Log Log Regression Statistics 12 1.6021 -0.5376 Multiple R 0.99999B R 5quare 0.999996 2.0000 13 2.0374 0.1038 0.4533 Adiusted R 0.9g9996 14 2.2718 1.5000 0.002343 1 0272 Obraruati 3 2605 1.0000 17 3.4094 2.1490 Series1 18 3.5272 2.3246 ANOVA 0.5000 ionificance 19 di MS 1358512 8.82F 15 0.0000 6 7.457418 22 Tota 0,0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 23 0.5000 Coefficientsandord Err tStat P-value Lower 95 %Upper 95%ower 95.0%pper 95.0% 24 25 0.0036 817.5785 2.9162 2.9162 Intercept 2.325 0.0000 2.9340 29540 -1.0000 xVariable 0.c013 1165.5521 4849 1.4915 1.4849 1.4915 The least square regression line of transformed data is y= 1.4882 x-2.9254 29 30 31 Sheett Sheet2 Sheet3 10oss Reagy 7:11 AM Type here to search G

a) The required scatter diagram is option C
b)
x   log x y   log y
40      1.6021      0.29    -0.5376
109 2.0374 1.27 0.1038
187   2.2718 2.84 0.4533
791       2.8982     24.39    1.3872
1822   3.2605    84.56    1.9272
2567   3.4094   140.93    2.1490
3367   3.5272    211.15   2.3246

The required scatter diagram is option D
c)
Least square regression line of transformed data is,
y = 1.4882 x -2.9254
d) Power equation of best fit is,
y = x^1.4882 * EXP(-2.9254)
y = x^1.4882 * 0.0536