In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ý = 17.6 + 3.4x, – 2.5x, + 7.9x3 + 2.9×4 (a) Interpret b, in this estimated regression equation. O b, = -2.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x2, X3, and x, are held constant. O b, = 3.4 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, = 7.9 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 b O b = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x3 are held constant. = 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x2, x3, and x, are held constant. Interpret b, in this estimated regression equation. O bz = -2.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x4 are held constant. b2 = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x4 when x,, x2, and x3 are held constant. = -2.5 is an estimate of the change in y corresponding to a 1 unit change in x2 when x, x3, and x, are held constant. b2 = 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x2, x3, and x, are held constant. %3D b2 = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x, are held constant. %3D Interpret b, in this estimated regression equation. O bz = 3.4 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 b3 = -2.5 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 bz = -2.9 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 bz = 7.9 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 bz = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2 and x4 are held constant. Interpret b, in this estimated regression equation. O b, = 7.9 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 b, = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X2, and x3 are held constant. O bą = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2 and x4 are held constant. %3D O bą = 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2 and x3 are held constant. %3D O b4 = -2.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, xX3, and x, are held constant. (b) Predict y when x, = 10, x, = 5, x3 = 1, and x4 = 2.
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.
Ў %3D 17.6 + 3.4х, - 2.5х, + 7.9х; + 2.9х4
(a) Interpret b, in this estimated regression equation.
O b, = -2.5 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, = 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant.
O b, = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x4 are held constant.
= 2.9 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 b1
= 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x, are held constant.
O b1
Interpret b, in this estimated regression equation.
b2
= -2.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x are held constant.
b2
= 2.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X2, and x3 are held constant.
b2
= -2.5 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 b2
= 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x, are held constant.
O b2
= 7.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x,, and x, are held constant.
Interpret b, in this estimated regression equation.
b3
= 3.4 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x,, and x, are held constant.
b3
= -2.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, X3, and x4 are held constant.
b3
= -2.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x,, and x3 are held constant.
O b3 = 7.9 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 bz = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x,, and x, are held constant.
3.
Interpret b, in this estimated regression equation.
O ba = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant.
4
O b, = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x3 are held constant.
4
O b4 = 2.9 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, = 3.4 is an estimate of the change in y corresponding to a 1 unit change in x.
when
and x, are held constant.
b4
= -2.5 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant.
(b) Predict y when x,
10, x, = 5, x3 = 1, and x.
= 2.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ea199ac-d9f9-432f-8dc8-6b9e2b6778a5%2F6abb5900-417b-4be1-b680-436efed0a5fc%2Fwiow3i_processed.png&w=3840&q=75)
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