Regression Leverage Formula (Jerry W. Lewis or Mike Middleton)already have DFITS formula
 

I have been trying to figure out the leverage formula for a set of X Y
values
X Y
75 16
83 20
85 25
85 27
92 32
97 48
99 48

Using the data analysis add-in and adding residuals then running
regression gives me Predicted Y, Residuals and Standard Residuals, If
my data was in A2:B8 (X and Y) and C2 housed this formula =SLOPE($B
$2:$B$8,$A$2:$A$8)*A2+INTERCEPT($B$2:$B$8,$A$2:$A$ 8) which gives me my
predicted y and D2 housed B2-C2 which gives me my residuals then E2
housed =D2*D2 which gives me my residuals squared. What I am looking
for in cell F2 is HI1(the weight of the leverage value (y value) for
the ith residual). I have the values for the Leverage but do not know
how they were derived.

F2:F8
0.53588
0.200997
0.163787
0.163787
0.180066
0.331229
0.424252

I have the DFITS formula in G2:
=D2*SQRT((7-2-1)/(SUM($E$2:$E$8)*(1-F2)-E2))*SQRT(F2/(1-F2))

But do not know how they derived the Leverage Formula?
Can you please give me some guidance?
Thanks in advance

Regression Leverage Formula (Jerry W. Lewis or Mike Middleton) already have DFITS formula
 

PJ -

Based on a Google search for "regression leverage" (without the quotes) and
the first item "Leverage and Influential points" at
http://www.stat.rutgers.edu/~saral/p...nfluential.pdf, the
desired values in your column F are equal to the h values shown on pages 17
and 18 of that document.

(An alternative equivalent formula for h is shown on page 12 as h = (1/n) +
p, where p is defined on page 2 of the document.)

For your data set, the variance of x is VARP(A2:A8) =61.42857.

Sum of squared deviations of x is n*VARP(A2:A8) = 430.

Xbar = 88, and for the first observation, x = 75, the deviation is -13 and
the squared deviation is 169.

The intermediate value p = squared deviation divided by sum of squared
deviations, so, for the first observation, p = 169/430 = 0.39302.

For the first observation, h = (1/n) + p = (1/7) + 0.39302 = 0.14286 +
0.39302 = 0.53588.

- Mike
http://www.MikeMiddleton.com



"PJ" wrote in message
...
I have been trying to figure out the leverage formula for a set of X Y
values
X Y
75 16
83 20
85 25
85 27
92 32
97 48
99 48

Using the data analysis add-in and adding residuals then running
regression gives me Predicted Y, Residuals and Standard Residuals, If
my data was in A2:B8 (X and Y) and C2 housed this formula =SLOPE($B
$2:$B$8,$A$2:$A$8)*A2+INTERCEPT($B$2:$B$8,$A$2:$A$ 8) which gives me my
predicted y and D2 housed B2-C2 which gives me my residuals then E2
housed =D2*D2 which gives me my residuals squared. What I am looking
for in cell F2 is HI1(the weight of the leverage value (y value) for
the ith residual). I have the values for the Leverage but do not know
how they were derived.

F2:F8
0.53588
0.200997
0.163787
0.163787
0.180066
0.331229
0.424252

I have the DFITS formula in G2:
=D2*SQRT((7-2-1)/(SUM($E$2:$E$8)*(1-F2)-E2))*SQRT(F2/(1-F2))

But do not know how they derived the Leverage Formula?
Can you please give me some guidance?
Thanks in advance

Regression Leverage Formula (Jerry W. Lewis or Mike Middleton)already have DFITS formula
 

On Jun 1, 8:06*pm, "Mike Middleton"
wrote:
PJ *-

Based on a Google search for "regression leverage" (without the quotes) and
the first item "Leverage and Influential points" athttp://www.stat.rutgers.edu/~saral/pdf/563/Leverages-influential.pdf, the
desired values in your column F are equal to the h values shown on pages 17
and 18 of that document.

(An alternative equivalent formula for h is shown on page 12 as h = (1/n) +
p, where p is defined on page 2 of the document.)

For your data set, the variance of x is VARP(A2:A8) =61.42857.

Sum of squared deviations of x is n*VARP(A2:A8) = 430.

Xbar = 88, and for the first observation, x = 75, the deviation is -13 and
the squared deviation is 169.

The intermediate value p = squared deviation divided by sum of squared
deviations, so, for the first observation, p = 169/430 = 0.39302.

For the first observation, h = (1/n) + p = (1/7) + 0.39302 = 0.14286 +
0.39302 = 0.53588.

- *Mikehttp://www.MikeMiddleton.com

"PJ" wrote in message

...



I have been trying to figure out the leverage formula for a set of X Y
values
X * * * * * * * *Y
75 16
83 20
85 25
85 27
92 32
97 48
99 48

Using the data analysis add-in and adding residuals then running
regression gives me Predicted Y, Residuals and Standard Residuals, If
my data was in A2:B8 (X and Y) and C2 housed this formula =SLOPE($B
$2:$B$8,$A$2:$A$8)*A2+INTERCEPT($B$2:$B$8,$A$2:$A$ 8) which gives me my
predicted y and D2 housed B2-C2 which gives me my residuals then E2
housed =D2*D2 which gives me my residuals squared. What I am looking
for in cell F2 is HI1(the weight of the leverage value (y value) for
the ith residual). I have the values for the Leverage but do not know
how they were derived.

F2:F8
0.53588
0.200997
0.163787
0.163787
0.180066
0.331229
0.424252

I have the DFITS formula in G2:
=D2*SQRT((7-2-1)/(SUM($E$2:$E$8)*(1-F2)-E2))*SQRT(F2/(1-F2))

But do not know how they derived the Leverage Formula?
Can you please give me some guidance?
Thanks in advance- Hide quoted text -

- Show quoted text -

Mike,

Thank you so much for your guidance and the link. Much appreciated.