B Com > Business Mathematics and Statistics > Regression coefficients - Correlation & Regression, Business Mathematics & Statistics
Regression coefficients - Correlation & Regression, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com
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FAQs on Regression coefficients - Correlation & Regression, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com
| 1. What are regression coefficients and how are they used in correlation and regression analysis? |  |
Ans. Regression coefficients are numerical values that represent the relationship between a predictor variable and a response variable in regression analysis. In correlation analysis, regression coefficients indicate the strength and direction of the linear relationship between two variables. These coefficients are used to estimate the value of the response variable based on the predictor variable(s) and can help in making predictions or understanding the impact of a predictor variable on the response variable.
| 2. How do you interpret regression coefficients in correlation and regression analysis? | |
Ans. The interpretation of regression coefficients depends on the context and the variables involved. In correlation analysis, a positive coefficient indicates a positive linear relationship between the variables, meaning that as one variable increases, the other tends to increase as well. A negative coefficient indicates an inverse relationship, where as one variable increases, the other tends to decrease.
In regression analysis, the coefficient represents the change in the response variable for a one-unit change in the predictor variable, holding other variables constant. For example, if the coefficient for a predictor variable is 0.5, it means that for every one-unit increase in the predictor variable, the response variable is expected to increase by 0.5 units.
| 3. How are regression coefficients calculated in correlation and regression analysis? | |
Ans. Regression coefficients are calculated using statistical methods such as least squares estimation. In correlation analysis, the coefficient is calculated as the covariance between the variables divided by the product of their standard deviations.
In regression analysis, the coefficients are estimated by minimizing the sum of the squared differences between the observed values of the response variable and the predicted values based on the predictor variable(s). This is done using mathematical formulas or software tools, such as Excel or statistical packages like R or SPSS.
| 4. What is the difference between correlation coefficients and regression coefficients? | |
Ans. Correlation coefficients measure the strength and direction of the linear relationship between two variables, without considering the cause-and-effect relationship. They range from -1 to +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
On the other hand, regression coefficients are specific to regression analysis and represent the impact of a predictor variable on the response variable, while controlling for other variables. They can be positive or negative and provide information about the direction and magnitude of the relationship between the variables.
| 5. How do you interpret the p-values associated with regression coefficients in correlation and regression analysis? | |
Ans. In correlation analysis, p-values are used to determine the statistical significance of the correlation coefficient. A p-value less than a chosen significance level (e.g., 0.05) indicates that the observed correlation is unlikely to have occurred by chance, suggesting a significant relationship between the variables.
In regression analysis, p-values associated with regression coefficients indicate whether the coefficient is statistically significant. A low p-value suggests that the coefficient is unlikely to be zero, meaning that there is evidence of a significant relationship between the predictor variable and the response variable. However, it is important to consider the context and the overall model fit when interpreting p-values in regression analysis.
Text Transcript from Video
Oh a welcome religion or linear
regression is perfect and now is it all
off starting calculations we have a case
and in which we are going to throw the
whole case in two parts in the first
part we are going to calculate the
coefficients of progression divisor SBS
life and Perficient of correlation and
then in the end we shall prove that the
Perficient of correlation is the
geometric mean of the two coefficients
of regulation and in the second part
next lecture or next video lectures we
shall say find out the equations of the
length of recognition and we shall also
find out estimated values of Y and X
respectively when some value is known of
x and y let us start we have a case with
two variables x and y and when you are
here let us first of all find out the
summation of these two original menus or
original variables and see the end of
the values he is very little we can use
these values directly for the purpose of
calculations but we need three more
columns three more solutions we want to
substitute in to formula as well as in
the formula of an improvement of
permission of four attorneys for in
summation Sigma X Sigma Y P Metroid
investor s Sigma Y square so let us find
out the summation of B 2 6 plus 2 8 10
plus + 18 + 4 32 + 8 30 Sigma X 30 that
means X bar will be 30 divided by n + 5
so it's ballistics so we can have
another how to let you to use the
formula or formula having the permission
of the variations datum from excluding
but this is the first case level
to use that formula we are going to use
the trait for Mira 1931 ridiculous by
twenty five plus eight thirty three plus
seven forty Sigma Y is 40 so I bar will
be 40 by n five survivor is eight mean
of X is six minified is a both are
integers it's in divide 6 into 9 54 2
into 11 22 10 into 5 54 into 8 32 18 to
7 56 and the total sum to to the red 43
Sigma XY X square 6 12 36 to square for
10 12 red for 12 16 8 / 54 so he comes
to 40 plus and a 140 plus 80 220 Sigma X
square 220 now we return of Y square
nice where 81 11 square 121 525 a 24/7
square 49 and its total comes to 340 ok
now we have all five innocence so we can
easily included all the three
coefficients let's start first is the
position or progression the memories of
Y on X will be by act and be my is and
Sigma XY minus Sigma X into Sigma Y upon
Sigma X square minus Sigma X whole
square see we can substitute these for
summations dieting the
will so I tell it is the idiot way to
find out the coefficient of regression
coefficients operators and every
coefficient of voltages because in all
other formulas we need some calculations
before returning the table
okay peyote R and Sigma XY is 214 minus
Sigma X is 30 Sigma Y is 40 upon and
Sigma X 25 into Sigma X vary 220 minus
50 square that is 1070 minus 100 200
upon 1100 minus 900 so tv-pg is minus
100 can be upon 200 so the verbage is no
progression of Y on it that is B by 8 is
minus point 6 5 it is minus point
another is the coefficient of regression
of X on Y that is B X Y which is the
formula of da twice the numerator
remains the same and Sigma XY minus
Sigma X into Sigma Y upon now Y is
independent variables we know mediator
is only made up of independent variables
n Sigma Y square minus Sigma Y the whole
square set a substitute the values ne5
214 minus 30 to 40 the saying you may
return upon now n 5 Sigma Y square e 340
minus 40 square so it is 1070 - 1200 and
over in the previous 8 342 5 1700 - 1600
so it is minus 150 of 1/100 so b XY e -
1.33 one of the coefficients of
regression is greater than 1 if we
ignore the sign another is left hand one
sign of both the coefficients must be
changed because Cyrene is dependent on
the numerator and only numerator can be
negative over positive is the numerator
is negative the signs of the Perficient
evil so negative now let us calculate
coefficient of correlation coefficient
of correlation is again the generator
and Sigma Y minus Sigma X into Sigma Y
monster denominators will be here but
with the sign of twelve upon under root
and Sigma X square
- Sigma at the square into under root
and Sigma Y square minus Sigma Y da
whole square all the way you will be
changed but the effect of these two
types of Beirut and their product is
very significant five into 214 - 30 into
40 upon under root 5 into 220 - a speech
where if you directly substitute the
values from these two rotated that is
also allowed because it is nothing but
the liquidation of the future of P
values 5 into 340 minus 40 square so it
is 1070 - 1200 in the numerator in the
denominator
BB's 1100 - 900 square root into under
root 1700 - 1600 so it will be minus 130
of 1 under root 200 into under root 100
now you have more than 100 available to
keep divide each one
yes - 130 divided by idle you can first
take the square root of these 2 and then
multiply them or you can multiply
therefore and Del theta square yes it
will be under root 20,000 so it is minus
150 divided by 140 1.4 - so the
coefficient of correlation is again
minus zero point nine one nine
approximately you can say it is minus
0.9 to treat the sine of all the three
coefficients is saying remember the
property the sign of coefficient of
the purpose of aggressive elated because
tiny dependent on numerator and the
numerator retain in all the three
formulas there twice design was beating
now we know that another properties the
product of the two coefficients of
regression is exactly equal to the
square of the two quadrature operators
therefore the coefficient of correlation
is square root of the product of the
coefficients of regression in other
words if we multiply two matrices and
add each square root it is called
geometric mean of the two vectors so
coefficient of correlation each
geometric mean of the quadratures of
witnesses let us get it with the with
use of divisor X and when B is 1 it is
minus 1 point 3 so it I must prove
maintain order
- point 6 5 into minus 1 point 3 so it
is under 0.8 4 5 under root point 8 4 5
okay so because there is it is positive
or negative square root of point eight
four five zero zero one two point nine
one nine yes what about these
whether because the square root of point
84 5 can either be negative or positive
what should be in this case since the
nine of the coefficients of Britain is
negative the sign of the coefficient of
correlation must made a review so
coefficient of correlation
- point nine one nine or - 0.92
opportunity C the answer of the purposes
of boilesen is the same we obtained
through two different methods but this
is the proof of the fact that the
coefficient of correlation is the
geometric mean of the two quadrature
operators so this was the EBS possible
rate who can collect the coefficients of
regression yes this was part one of the
solution of this case in the next
lecture we are going to cover the
process of finding the lines of
regression or the equations of the
length of regression for the paintings
with the help of these form is at X bar
Y bar VX NBA at it thank you
regression is perfect and now is it all
off starting calculations we have a case
and in which we are going to throw the
whole case in two parts in the first
part we are going to calculate the
coefficients of progression divisor SBS
life and Perficient of correlation and
then in the end we shall prove that the
Perficient of correlation is the
geometric mean of the two coefficients
of regulation and in the second part
next lecture or next video lectures we
shall say find out the equations of the
length of recognition and we shall also
find out estimated values of Y and X
respectively when some value is known of
x and y let us start we have a case with
two variables x and y and when you are
here let us first of all find out the
summation of these two original menus or
original variables and see the end of
the values he is very little we can use
these values directly for the purpose of
calculations but we need three more
columns three more solutions we want to
substitute in to formula as well as in
the formula of an improvement of
permission of four attorneys for in
summation Sigma X Sigma Y P Metroid
investor s Sigma Y square so let us find
out the summation of B 2 6 plus 2 8 10
plus + 18 + 4 32 + 8 30 Sigma X 30 that
means X bar will be 30 divided by n + 5
so it's ballistics so we can have
another how to let you to use the
formula or formula having the permission
of the variations datum from excluding
but this is the first case level
to use that formula we are going to use
the trait for Mira 1931 ridiculous by
twenty five plus eight thirty three plus
seven forty Sigma Y is 40 so I bar will
be 40 by n five survivor is eight mean
of X is six minified is a both are
integers it's in divide 6 into 9 54 2
into 11 22 10 into 5 54 into 8 32 18 to
7 56 and the total sum to to the red 43
Sigma XY X square 6 12 36 to square for
10 12 red for 12 16 8 / 54 so he comes
to 40 plus and a 140 plus 80 220 Sigma X
square 220 now we return of Y square
nice where 81 11 square 121 525 a 24/7
square 49 and its total comes to 340 ok
now we have all five innocence so we can
easily included all the three
coefficients let's start first is the
position or progression the memories of
Y on X will be by act and be my is and
Sigma XY minus Sigma X into Sigma Y upon
Sigma X square minus Sigma X whole
square see we can substitute these for
summations dieting the
will so I tell it is the idiot way to
find out the coefficient of regression
coefficients operators and every
coefficient of voltages because in all
other formulas we need some calculations
before returning the table
okay peyote R and Sigma XY is 214 minus
Sigma X is 30 Sigma Y is 40 upon and
Sigma X 25 into Sigma X vary 220 minus
50 square that is 1070 minus 100 200
upon 1100 minus 900 so tv-pg is minus
100 can be upon 200 so the verbage is no
progression of Y on it that is B by 8 is
minus point 6 5 it is minus point
another is the coefficient of regression
of X on Y that is B X Y which is the
formula of da twice the numerator
remains the same and Sigma XY minus
Sigma X into Sigma Y upon now Y is
independent variables we know mediator
is only made up of independent variables
n Sigma Y square minus Sigma Y the whole
square set a substitute the values ne5
214 minus 30 to 40 the saying you may
return upon now n 5 Sigma Y square e 340
minus 40 square so it is 1070 - 1200 and
over in the previous 8 342 5 1700 - 1600
so it is minus 150 of 1/100 so b XY e -
1.33 one of the coefficients of
regression is greater than 1 if we
ignore the sign another is left hand one
sign of both the coefficients must be
changed because Cyrene is dependent on
the numerator and only numerator can be
negative over positive is the numerator
is negative the signs of the Perficient
evil so negative now let us calculate
coefficient of correlation coefficient
of correlation is again the generator
and Sigma Y minus Sigma X into Sigma Y
monster denominators will be here but
with the sign of twelve upon under root
and Sigma X square
- Sigma at the square into under root
and Sigma Y square minus Sigma Y da
whole square all the way you will be
changed but the effect of these two
types of Beirut and their product is
very significant five into 214 - 30 into
40 upon under root 5 into 220 - a speech
where if you directly substitute the
values from these two rotated that is
also allowed because it is nothing but
the liquidation of the future of P
values 5 into 340 minus 40 square so it
is 1070 - 1200 in the numerator in the
denominator
BB's 1100 - 900 square root into under
root 1700 - 1600 so it will be minus 130
of 1 under root 200 into under root 100
now you have more than 100 available to
keep divide each one
yes - 130 divided by idle you can first
take the square root of these 2 and then
multiply them or you can multiply
therefore and Del theta square yes it
will be under root 20,000 so it is minus
150 divided by 140 1.4 - so the
coefficient of correlation is again
minus zero point nine one nine
approximately you can say it is minus
0.9 to treat the sine of all the three
coefficients is saying remember the
property the sign of coefficient of
the purpose of aggressive elated because
tiny dependent on numerator and the
numerator retain in all the three
formulas there twice design was beating
now we know that another properties the
product of the two coefficients of
regression is exactly equal to the
square of the two quadrature operators
therefore the coefficient of correlation
is square root of the product of the
coefficients of regression in other
words if we multiply two matrices and
add each square root it is called
geometric mean of the two vectors so
coefficient of correlation each
geometric mean of the quadratures of
witnesses let us get it with the with
use of divisor X and when B is 1 it is
minus 1 point 3 so it I must prove
maintain order
- point 6 5 into minus 1 point 3 so it
is under 0.8 4 5 under root point 8 4 5
okay so because there is it is positive
or negative square root of point eight
four five zero zero one two point nine
one nine yes what about these
whether because the square root of point
84 5 can either be negative or positive
what should be in this case since the
nine of the coefficients of Britain is
negative the sign of the coefficient of
correlation must made a review so
coefficient of correlation
- point nine one nine or - 0.92
opportunity C the answer of the purposes
of boilesen is the same we obtained
through two different methods but this
is the proof of the fact that the
coefficient of correlation is the
geometric mean of the two quadrature
operators so this was the EBS possible
rate who can collect the coefficients of
regression yes this was part one of the
solution of this case in the next
lecture we are going to cover the
process of finding the lines of
regression or the equations of the
length of regression for the paintings
with the help of these form is at X bar
Y bar VX NBA at it thank you
About this Video
|
4.73/5 Rating |
|
Arshit Thakur |
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