Question

1. Create a scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’. Include the trendline, the equation of the trendline, and the coefficient of determination on the graph.
2. Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X. Hint from Dr. Klotz: You can get this right from the trendline.
3. Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.
4. Conduct a full hypothesis test:   You will be in charge. Set your own significance level. The hypotheses are given.
   • H0: β1 = 0
   • Ha: β1 ≠ 0
   • Hint: Remember that a full hypothesis test is more than running the data analysis program. What were the steps from last week's discussion?
5. In a highlighted box, discuss your final conclusion from this hypothesis test. For each major, is Annual % ROI related to Cost for business? For engineering? If so, describe the relationship in words. How does the outcome of this hypothesis test related to the central question of which ROI is better?
6. Business major info is listed below:

7. School Type	Cost	30 Year ROI	Annual ROI
   Private	$222,700.00	$1,786,000.00	7.70%
   Private	$176,400.00	$1,758,000.00	8.40%
   Private	$212,200.00	$1,714,000.00	7.80%
   Public	$125,100.00	$1,535,000.00	9.10%
   Private	$212,700.00	$1,529,000.00	7.40%
   Public	$92,910.00	$1,501,000.00	10.10%
   Private	$214,900.00	$1,485,000.00	7.30%
   Private	$217,800.00	$1,483,000.00	7.20%
   Private	$225,600.00	$1,444,000.00	7.00%
   Private	$217,300.00	$1,442,000.00	7.10%
   Private	$226,500.00	$1,441,000.00	7.00%
   Private	$215,500.00	$1,438,000.00	7.20%
   Private	$223,500.00	$1,428,000.00	7.00%
   Private	$226,600.00	$1,414,000.00	7.00%
   Private	$189,300.00	$1,397,000.00	7.50%
   Public	$89,700.00	$1,382,000.00	9.90%
   Public	$87,030.00	$1,376,000.00	10.00%
   Private	$218,200.00	$1,343,000.00	6.90%
   Private	$229,900.00	$1,339,000.00	6.70%
   Private	$148,800.00	$1,321,000.00	8.10%

Answer 1

Sol:

In excel got to insert scatterchart

Book1 - Excel X Chart Tools Share Page Layout Formulas Tell me what you want to do. Adabala Naveenkumarvenkat File Home Insert Data Review View Design Format A TT Equation Store 1? Symbol PivatTable W Line Column Wina Pictures Slicer Timeline Hyperlink Table My Add-ins - Recommended Pivotchart Charts Man Box Loss llustrations Add-ins Links Tables Charts Tours Sparklitnes Filters Symbols Insert Pie or Doughnut Chart A D K L M N P Use this chart 1 School Tvoe Cost Annual ROL Annual ROL 30 Year ROL portions of a whole. Use it when 2 Prvate 7.70 222.700 0 1786000 770% 222,70 the tota your numbers is 100 % 3 Privato 8.40 17640 1758000 8.40% + 21 Click the amow to see the different 12.00 4 Prvate 7.80 21220 1714000 78058 9.10 types of pie and doughnut charts 5 Public 12510 1530000 9.10% 10.00 7,40 6 Private 212700 1529000 740% the icons to see a preview in your 9291 7 Public 10.10 1501000 10.10% dooument. 21. 8.00 7.30 8 Private 7.30 21490 148500 7.20 9 Private 7.20 21780 1483000 7 20% 217805 6.00 10 Prvate 7.00 7.00 22560 1444000 7.0058 225605 7.10 217300 11 Prvate 7.10 7.10 1442000 21730 4.00 12 Prvate 7.00 7.00 22550 1441000 7.0058 22600 7.20 2.00 215500 13 Private 7.20 7.20 2150 1438000 14 Pivate 223500 7.00 7.00 22302 1428000 7.0058 0.00 15 Private 7.00 7.00 22660 1414000 7.0058 228607 0,00 50,000.00 100,000.00 150,000.00 200,000.00 250.000.00 7.50 16 Prvate 7.50 7.50 18930 1397000 180000 Cost 9.90 17 Public 9.90 9.90 8970: 89700 1382000 18 Publia 10.00 10.00 8708 1376000 10.00% 8703) 6.90 19 Private 6.90 6.90 218200 1343000 218205 20 Private 6.70 6.70 229900 1339000 6.70% 2290 8.10 1321008 8.10 21 Prvate 8.105% 148800 148800 22 23 Sheet 12 Sheet13 Sheet8 Sheet9 . Sheet4 Sheet6 Sheet5 Sheet2 Sheet7 Sheet10 Ready Scroll Lock Average: 94319.91 Min: 6.7 + 100% Count 42 Max 229900 Sum: 37727964 9:45 AM O Type here to search 6/27/2019 Annual RO

12.00 10.00 8.00 y=-2E-05x+ 11.804 R2= 0.941 6,00 4,00 2.00 0.00 150,000.00 0.00 50,000.00 100,000.00 200,000.00 250,000.00 COST ANNUAL ROI

From scatterplot we get

from:linear

strength:strong

Direction:negative

Solution2:

1. Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X. Hint from Dr. Klotz: You can get this right from the trendline.

In excel go to data >data analysis>regression

You will get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.970065
R Square	0.941026
Adjusted R Square	0.93775
Standard Error	0.274342
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	21.61726	21.61726	287.2207	1.64E-12
Residual	18	1.354744	0.075264
Total	19	22.972
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	11.80399	0.242949	48.58621	1.51E-20	11.29357	12.31441
Cost	-2.1E-05	1.25E-06	-16.9476	1.64E-12	-2.4E-05	-1.9E-05

you will get

b0= y intrcept=11.80399

b1=slope=-2.1E-05=-0.000021

Regression equation is

Annual ROI=11.80399-0.000021*Cost

Solution3:

we have

Regression equation is

Annual ROI=11.80399-0.000021*Cost

=11.80399-0.000021*160000

=8.44399

=8.44%

ANSWER:8.44%