Question

Q2). The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

Height (in feet)	Stories
1050	56
428	29
362	25
529	40
790	60
401	22
380	38
1454	110
1127	100
700	46

Part (a) Using "stories" as the independent variable and "height" as the dependent variable, make a scatter plot of the data

Part (b) Does it appear from inspection that there is a relationship between the variables?

Yes

No     

Part (c) Calculate the least squares line. Put the equation in the form of: ? = a + bx. (Round your answers to three decimal places.)

? = +   x

Part (d) Find the correlation coefficient r. (Round your answer to four decimal places.)

r =  

Is it significant?

Yes

No     

Part (e) Find the estimated height for 31 stories. (Use your equation from part (c). Round your answer to one decimal place.)

( ) ft

Find the estimated height for 98 stories. (Use your equation from part (c). Round your answer to one decimal place.)
( ) ft

Part (f) Use the two points in part (e) to plot the least squares line. (Upload your file below.)

Part (g) Based on the above data, is there a linear relationship between the number of stories in tall buildings and the height of the buildings?

Yes

No     

Part (h) Are there any outliers in the above data? If so, which point(s)?

No, there are no outliers.

Yes, (56, 1050) and (22, 401) are outliers.     

Yes, (22, 401) is an outlier.

Yes, (56, 1050) is an outlier.

Part (i) What is the estimated height of a building with 9 stories? (Use your equation from part (c). Round your answer to one decimal place.

( ) ft

Does the least squares line give an accurate estimate of height? Explain why or why not.

The estimate for the height of a nine-story building does not make sense in this situation.

The least squares regression line does not give an accurate estimate because the estimated height of a building with nine stories is not within the range of y-values in the data.     

The least squares regression line does not give an accurate estimate because a nine-story building is not within the range of x-values in the data.

The least squares regression line does give an accurate estimate because none of the buildings surveyed had nine stories.

Part (j) Based on the least squares line, adding an extra story adds about how many feet to a building? (Round your answer to three decimal places.)

( ) ft

Part (k) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)

Interpret the slope.

As the -Select- ( number of stories or height) of the building increases by one unit, the  -Select- (number of stories or height) of the building increases by -Select- (stories or feet) .

Answer 1

Part (a)

(b) Yes there is a linear upward relationship between variables.

(c) The regression output is given below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.941134
R Square	0.885733
Adjusted R Square	0.87145
Standard Error	135.5212
Observations	10
ANOVA
	df	SS	MS	F
Regression	1	1138903	1138903	62.01147
Residual	8	146928	18366
Total	9	1285831
	Coefficients	Standard Error	t Stat	P-value
Intercept	105.1416	89.30164	1.177376	0.272883
Stories	11.72925	1.489478	7.874736	4.89E-05

y^ =105.1416 + 11.7293 x

Correlation coefficient r = 0.9411

(e) Here x = 31 stories

y^(31) =105.1416 + 11.7293 * 31 = 468.75

y^(98) = 105.1416 + 11.7293 * 98 = 1254.61

(f) yes, there is a linear relationship.

(g) There is no outlier.

(i)

x = 9

y^(98) = 105.1416 + 11.7293 * 9 = 210.7053

(j) The least squares regression line does not give an accurate estimate because a nine-story building is not within the range of x-values in the data.

(k) Slope here = 11.7293

As the number of stories of the building increases by one unit, the height of the building increases by 11.7293  feet) .