1. A researcher wants to know if there is a relationship between the heights (si
ID: 3314229 • Letter: 1
Question
1. A researcher wants to know if there is a relationship between the heights (sidewalk to roof) of notable tall buildings (measured in feet) in America the number of stories of the building (beginning at street level). The researcher is trying to predict height using the number of stories. Use the output below and the fact that R2 = 0.890 to answer the following questions.
a. Interpret the slope in the words of the problem.
b. Find coefficient of determination and interpret its meaning in the words of the problem.
c. Find correlation coefficient and interpret its meaning in the words of the problem.
d. Is the true slope significantly different from 0? Justify!
e. If the building with 60 stories has a height of 790 feet, find the residual.
Coefficients
Standard Error
t Stat
P - value
Lower 95%
Upper 95%
Intercept
102.4287
87.60613
1.169195
0.27598
- 99.5914
304.4488
Stories
11.75847
1.459029
8.059108
4.14E - 05
8.393943
15.123
Coefficients
Standard Error
t Stat
P - value
Lower 95%
Upper 95%
Intercept
102.4287
87.60613
1.169195
0.27598
- 99.5914
304.4488
Stories
11.75847
1.459029
8.059108
4.14E - 05
8.393943
15.123
Explanation / Answer
a) Slope = 11.75847
As the number stories increase 1 then the height is also increase 11.75847 units
b) coefficient of determination = 0.890 = 89% of variation in heights can explained by the stories
c) correlation coefficient = sqrt(0.890) = 0.9433
d) H0: population slope is zero
H1: population slope not is zero
P-value of slope = 0.000< alpha 0.05, so we reject H0
Thus we conclude that population slope not is zero
e)
If X 60 stories then
Y-hat = 102.4257 + 11.75847(60) = 807.9339
Residual = 790 - 807.9339 = -17.9339
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