3. A land-use planner observed that in popu Equation CI) can be converted into t
ID: 3321600 • Letter: 3
Question
3. A land-use planner observed that in popu Equation CI) can be converted into the a city the number of gas stations (y) in relation to the equivalent linear form shown in Equation (2). Using the s for a lation (x) could be described by Equation (1) were and are curve fitting parameters. lin of the equation, find the values of and using city with a population of data below and the equivalent linear form nun 4200 people? In y = ln + fix Populatio 1000 5000 2000 3500 4000 500 6000 2500 7000 1500 n (x) Number of Gas Stations 4 10 2 17 6 27Explanation / Answer
Regression Analysis
r²
0.955
n
10
r
0.977
k
1
Std. Error
0.173
Dep. Var.
lny
ANOVA table
Source
SS
df
MS
F
p-value
Regression
5.06820757
1
5.06820757
169.00
1.16E-06
Residual
0.23991027
8
0.02998878
Total
5.30811784
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
0.8790
0.1028
8.548
2.70E-05
0.6419
1.1162
x
0.00034292
0.00002638
13.000
1.16E-06
0.00028209
0.00040374
The regression model is
Ln y = 0.8790+0.00034292*x
Ln =0.8790
=2.408
The regression model is
y=2.408 exp(0.00034292*x)
when x=4200,
predicted y =2.408* exp(0.00034292*4200)
=10.166119
=10 ( rounded to whole number)
Regression Analysis
r²
0.955
n
10
r
0.977
k
1
Std. Error
0.173
Dep. Var.
lny
ANOVA table
Source
SS
df
MS
F
p-value
Regression
5.06820757
1
5.06820757
169.00
1.16E-06
Residual
0.23991027
8
0.02998878
Total
5.30811784
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
0.8790
0.1028
8.548
2.70E-05
0.6419
1.1162
x
0.00034292
0.00002638
13.000
1.16E-06
0.00028209
0.00040374
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