Nicol_Quijandria_Lab_3
xlsx
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School
Fashion Institute Of Technology *
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Course
222
Subject
Mathematics
Date
Apr 3, 2024
Type
xlsx
Pages
6
Uploaded by PrivateDragonflyPerson1076
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.96256
R Square
0.926521
Adjusted R
0.920398
Standard E
116.9612
Observatio
14
ANOVA
df
SS
MS
F
ignificance F
Regression
1
2069934
2069934 151.3118 3.668E-08
Residual
12 164159.1 13679.93
Total
13
2234093
Coefficients
andard Erro
t Stat
P-value
Lower 95%Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
128.0033 108.3619 1.181257 0.260383 -108.0971 364.1036 -108.0971 364.1036
X Variable 1.111399 0.090351 12.30088 3.668E-08
0.91454 1.308257
0.91454 1.308257
Y ( dependent)
X ( independent)
Rent
Size
950
850
1600
1450
1200
1085
1500
1232
950
718
1700
1485
1650
1136
935
726
875
700
1150
956
1400
1100
1650
1285
2300
1985
1800
1369
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.96255955931
R Square
0.92652090521
Adjusted R Sq 0.92039764731
Standard Erro 116.961218934
Observations
14
ANOVA
df
SS
MS
F
ignificance F
Regression
1 2069933.73632831
2069934 151.3118 3.668E-08
Residual
12 164159.120814543 13679.93
Total
13 2234092.85714286
Coefficients
Standard Error
t Stat
P-value
Lower 95%Upper 95%
Lower 95.0%
Intercept
128.003262789 108.361932493893 1.181257 0.260383 -108.0971 364.1036 -108.0971
X Variable 1
1.11139853959 0.09035110868087 12.30088 3.668E-08
0.91454 1.308257
0.91454
Rent_hat = 128.003 + 1.111* Size
y^= b0(y-intercept)+b1(slope)X
600
800
1000
1200
0
500
1000
1500
2000
2500
f(x) = 1.1113985395877 x + 128.0
R² = 0.926520905212291
Rent v
1 Which variable is your independent/explanatory and which your dependent/response?
Rent is the dependent variable, and Size is the independent variable.
2 Construct a scatterplot of the data putting the appropriate variable on the appropriate axis The graph shows a postive, moderatly strong correlation, because R closer to 1.
3 Report the values for b0 and for b1 from the Analysis Output and then write the least-squar
Rent hat= 128.003+1.111 (size)
4 Test Ho: β1=0 versus H1: β1≠0 at 0.05 level of significance. From this result determine whet
Based on the results apartment size and rent do have a significant relationship because the 5 Report R2, the Coefficient of Determination, and interpret it.
r2= 0.926520905212291 , strong linear relationship between X and Y majority of the variatio
6 Use the regression model you learned from question 3 to predict the Rent for a (i) 950 ft2 an
Rent hat= 1183.453 (950 ft.)
Rent hat=
1794.503 (1500 ft.)
7 Plot the least squares regression line on the original scatterplot you created in question 2.
on graph.
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Upper 95.0%
364.1036
1.308257
1400
1600
1800
2000
2200
003262789179
vs. Size
and calculate r, the correlation coefficient, using Excel function =correl(). Describe the direction and strengt
R=
0.96256
res equation in Ŷ = b0 + b1X form. Don’t use y and x use “Size” and “Rent” in the equation.
ther an apartment’s rent has a significant linear relationship with an apartment’s size.
P-value is less than the level of significance therefore H1: β1≠0 at 0.05 level of significance is true.
on in Y is explained by variation in X
nd (ii) 1500 ft2 apartment.
th of the relationship.
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