In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 16.7 + 3.5x, - 2.4x2 + 7.6x3 + 2.6x4 (a) Interpret b, in this estimated regression equation. = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant. O b, = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant. O b, = 7.6 is an estimate of the change in y corresponding to a 1 unit change in x3 when x,, x2, and x4 are held constant. O b, = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x4 when x,, x2, and x3 are held constant. O b, = -2.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant. Interpret b, in this estimated regression equation. O b2 = -2.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x4 are held constant. O b, = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x4 are held constant. O b, = 7.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X2, and x4 are held constant. O b, = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x4 when x,, x2, and xz are held constant. O b, = -2.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x4 are held constant. Interpret b, in this estimated regression equation. O bz = 7.6 is an estimate of the change in y corresponding to a 1 unit change in x3 when x,, x,, and xg are held constant. O b3 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x3 when x,, x,, and x4 are held constant. O b3 = -2.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x4 are held constant. O b3 = -2.6 is an estimate of the change in y corresponding to a 1 unit change in x4 when x,, x2, and x3 are held constant. O bz = 7.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x, are held constant. Interpret b, in this estimated regression equation. O ba = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x, are held constant. O ba = 3.5 is an estimate of the change in y corresponding to a 1 unit change in xa when x,, x2, and x3 are held constant. O ba = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x4 are held constant. O b4 = 7.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x3 are held constant. O ba = -2.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![In a regression analysis involving 30 observations, the following estimated regression equation was obtained.
ŷ = 16.7 + 3.5x1 – 2.4x2 + 7.6x3 + 2.6×4
(a) Interpret b, in this estimated regression equation.
b1
= 3.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x, are held constant.
bị
3.5 is an estimate of the change in y corresponding to a 1 unit change in
X1
when
X2, X31
and
X4 are held constant.
%D
b1
= 7.6 is an estimate of the change in y corresponding to a 1 unit change in
X3
when
X1, X21
and
X4
are held constant.
b1
2.6 is an estimate of the change in y corresponding to a 1 unit change in
X4
when
X1, X2,
and
X3 are held constant.
%D
= -2.4 is an estimate of the change in y corresponding to a 1 unit change in x,
when
X31
b1
and
X4
are held constant.
Interpret b, in this estimated regression equation.
b2
= -2.4 is an estimate of the change in y corresponding to a 1 unit change in
X2
when
X1, X31
and
Xa are held constant.
b2 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in
X1
when
X2, X31
and
X4 are held constant.
b2
= 7.6 is an estimate of the change in y corresponding to a 1 unit change in x3 when x,,
and
Xa are held constant.
b2 =
= 2.6 is an estimate of the change in y corresponding to a 1 unit change in
X4
when
X1, X21
and
X, are held constant.
b2
= -2.4 is an estimate of the change in y corresponding to a 1 unit change in x,
when
X2, X31
and x4
are held constant.
Interpret b, in this
stimated regression equation.
O b3 = 7.6 is an estimate of the change in y corresponding to a 1 unit change in
X3
when
X1, X21
and
X4
are held constant.
b3
3.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,,
and
Xa are held constant.
b3
= -2.4 is an estimate of the change in y corresponding to a 1 unit change in
X1
when
X2, X31
and
X4 are held constant.
b3 =
= -2.6 is an estimate of the change in y corresponding to a 1 unit change in x4
when
X1, X21
and x, are held constant.
b3
7.6 is an estimate of the change in y corresponding to a 1 unit change in
X2
when
X1, X31
and
X4
are held constant.
%D
Interpret b, in this estimated regression equation.
b4
= 2.6 is an estimate of the change in y corresponding
a 1 unit change in
when
X1'
X21
and
X3
are held constant.
= 3.5 is an estimate of the change in y corresponding to a 1 unit change in
b4
X4
when
X1, X21
and
X3
are held constant.
b4
= 2.6 is an estimate of the change in y corresponding to a 1 unit change in
X3
when
X1, X2, and X4 are held constant.
b4
7.6 is an estimate of the change in y corresponding to a 1 unit change in
X2
when
X1, X31
and
X3 are held constant.
%D
D4
= -2.4 is an estimate of the change in y corresponding to a 1 unit change in
X, when
X31
and
are held constant.
O O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96e0847f-4973-4b99-ac1e-7e94417321c7%2F33d9e983-2f61-4327-aced-960c8fd86aaa%2Fx9yadgu_processed.png&w=3840&q=75)
![(b) Predict
y when
10, x2 = 5, X3 :
X1
1, and
X4
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96e0847f-4973-4b99-ac1e-7e94417321c7%2F33d9e983-2f61-4327-aced-960c8fd86aaa%2Ffai91tj_processed.png&w=3840&q=75)
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