Question

In: Statistics and Probability

X Miami, is a residential tower (or a social living community as it's marketed) in Edgewater....

X Miami, is a residential tower (or a social living community as it's marketed) in Edgewater. It is designed around 2 principals: 1. Life's better with company and 2. You deserve to love your home. X Miami has rooftop yoga, a pool deck, and a "meet your neighbor" page on their website as means to facilitate social connection. The carefully curated tower took exceptionally long to build. To inform construction timelines of future social living communities in Miami, the board is interested in analyzing construction (feet) as a function of time (day). Assume the variables are linearly related.

July 2019 Day	Height of Construction (feet)
18	165
8	60
11	90
4	10
16	145
6	30
13	110

Would a scatterplot be an appropriate graph to visualize the data? If so, why? If appropriate, sketch a graph of the data.

Calculate the prediction equation for the regression of Y on X. Interpret each of the coefficients.

Define: (a) Y'₁₈ (b) Y₁₈. Interpret these values.

d. Define Y'₂₀

r²= .998. Interpret this value. Explain why this value is so high.

Expert Solution

a)

b)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
18	165	51.0204	6061.7347	556.1224
8	60	8.1633	736.7347	77.5510
11	90	0.0204	8.1633	0.4082
4	10	47.0204	5951.0204	528.9796
16	145	26.4490	3347.4490	297.5510
6	30	23.5918	3265.3061	277.5510
13	110	4.59	522.44898	48.9796

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	76.00	610.00	160.86	19892.86	1787.14
mean	10.86	87.14	SSxx	SSyy	SSxy

sample size ,   n =   7
here, x̅ = Σx / n=   10.857   ,     ȳ = Σy/n =   87.143

SSxx =    Σ(x-x̅)² =    160.8571
SSxy=   Σ(x-x̅)(y-ȳ) =   1787.1

estimated slope , ß1 = SSxy/SSxx =   1787.1   /   160.857   =   11.11012

intercept,   ß0 = y̅-ß1* x̄ =   -33.48135

so, regression line is   Ŷ =   -33.481   +   11.110   *x

c)

a) Predicted Y at X= 18 is
Ŷ = -33.4813 + 11.1101 *18= 166.501

b) Y18 = observed value of Y at x 18 = 165

d)

Predicted Y at X= 20 is
Ŷ = -33.4813 + 11.1101 *20= 188.721

R²=0.998

99.8% of variation in observation of variable Y is explained by variable X

High values indicates that data is good fit for linear relationship

orchestra answered 1 year ago

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