Question

In: Statistics and Probability

Create a scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’. Include the...

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.
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.
Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.
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?
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?
Business major info is listed below:

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%

Solutions

Expert Solution

Sol:

In excel got to insert scatterchart

From scatterplot we get

from:linear

strength:strong

Direction:negative

Solution2:

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%

orchestra answered 1 year ago

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