Q2). The height (sidewalk to roof) of notable tall buildings in America is compa
ID: 3376178 • Letter: Q
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).
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) .
Height (in feet) Stories 1050 56 428 29 362 25 529 40 790 60 401 22 380 38 1454 110 1127 100 700 46Explanation / Answer
Solution
NOTE
Answers to the point are given below. Details follow at the end.
Taking storeys as the independent variable, x and height as the dependent variable, y.
Estimated regression equation: ycap = 105.142 + 11.729x ANSWER 1
Correlation coefficient, r = 0.9411 ANSWER 2 and it is
significant even at a very low level of significance, p-value =4.8913 E – 05 ANSWER 3
Estimated height of the building with 31 storeys = 468.7 ANSWER 4
Estimated height of the building with 98 storeys = 1254.6 ANSWER 5
[Above two answers are obtained by substituting x = 31 and 98 respectively in Answer 1
Details
Data
i
xi
yi
1
56
1050
2
29
428
3
25
362
4
40
529
5
60
790
6
22
401
7
38
380
8
110
1454
9
100
1127
10
46
700
Calculations
n
10
xbar
52.60
ybar
722.1
Sxx
8278.4
Syy
1285830.9
Sxy
97099.4
?1cap
11.7292472
?0cap
105.141597
r
0.94113389
r^2
0.885733
Test for significance of r
t = r?{(n - 2)/(1 - r2)}
1- r^2
0.114267
(n-2)/(1-r^2)
70.0114667
sqrt
8.3672855
tcal
7.87473597
tcrit
2.30600413
p-value
4.8913E-05
DONE
i
xi
yi
1
56
1050
2
29
428
3
25
362
4
40
529
5
60
790
6
22
401
7
38
380
8
110
1454
9
100
1127
10
46
700
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