5. The height (sidewalk to roof of notable tall buildings in America is compared
ID: 3233156 • Letter: 5
Question
5. 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). Stories, x Height (in feet), y Tall Buildings in America 1,050 2,000 28 428 1500 26 362 1.000 529 500 790 20 40 60 80 100 120 22 401 Stories 380 110 1,454 100 1,127 46 700 a. Looking at the scatter plot of the data, does it appear that there is a linear relationship between the data? so, what the "direction" of this relationship? b. Calculate the least squares line a bx: c. Find the correlation coefficient, r d. use the P-value to test the significance of the correlation coefficient. Use a significance level of 5%. P value a Decision regarding Ho: Conclusion:Explanation / Answer
Answer:
a). There appears that there is linear relation between height and stories. The direction is positive.
b). The regression line y=102.4287+11.7585*x
c). r=0.944
d). P=0.000 < 0.05.
Reject Ho.
There is significant correlation between heights and stories.
e).
when x=32,
predicted y =102.4287+11.7585*32 =478.7007.
when x=94,
predicted y =102.4287+11.7585*94 =1207.728
f).
se=132.764.
g).
slope=11.7585
when stories increases by 1, the height increases by 11.7585 feet.
h).
r2 = 0.890
89% of variation in height is explained by stories.
Regression Analysis
r²
0.890
n
10
r
0.944
k
1
Std. Error
132.764
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,144,819.8376
1
1,144,819.8376
64.95
4.14E-05
Residual
141,011.0624
8
17,626.3828
Total
1,285,830.9000
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
102.4287
87.6061
1.169
.2760
-99.5914
304.4488
x
11.7585
1.4590
8.059
4.14E-05
8.3939
15.1230
Regression Analysis
r²
0.890
n
10
r
0.944
k
1
Std. Error
132.764
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,144,819.8376
1
1,144,819.8376
64.95
4.14E-05
Residual
141,011.0624
8
17,626.3828
Total
1,285,830.9000
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
102.4287
87.6061
1.169
.2760
-99.5914
304.4488
x
11.7585
1.4590
8.059
4.14E-05
8.3939
15.1230
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.