(a) The table below shows the age of children and the number of words recalled in a memory game. Age Number of Words Recalled 3 5 2 4 5 5 ) Based on the data above, find the linear regression equation to predict the number of words recalled from their age. (1 Calculate the predicted Y value for each of the X value

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Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
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q2  can you show every step on how to do the question do that I can understand the steps clearly. Also attached the regression . please use this formula ya

(a) The table below shows the age of children and the number of words recalled in a memory game.
Age
Number of Words Recalled
3
5
4
5
6
4
6
(1) Based on the data above, find the linear regression equation to predict the number of words
recalled from their age.
(1) Calculate the predicted Y value for each of the X value
Transcribed Image Text:(a) The table below shows the age of children and the number of words recalled in a memory game. Age Number of Words Recalled 3 5 4 5 6 4 6 (1) Based on the data above, find the linear regression equation to predict the number of words recalled from their age. (1) Calculate the predicted Y value for each of the X value
Regression Steps
STEP 1 PEARSON CORRELATION FIND r VALUE
STEP 2 REGRESSION
Regression function
Σx ΣΥ = Σxy -
ỹ = a + bx
Σχ2ΣΥ2 :
N =
ExEy
SP -Σxy -
Slope b regression of line
SP
n
(Ey)?
b
SSx
SSy = Ey2
n
(Σx)2
Y intercept a of regression line
SSy Σχ2
а — Му — ьмх
– bMx
à =
SP
r =
(SSx)(SSy)
STEP 3
F RATIO HYPOTHESIS TESTING REGRESSIION STANDARD ERROR OF ESTIMATE
STEP4
но-
SS resi dual
п — 2
SS regression =r2 SSy
SS residual = (1-r^2 XSSY )
Df regression
Df residual =n – 2
(Numerator)
(denominator)
MS regression = (SS regression)/df regression)
MS residual = (SS residual)/(df residual)
F= (MS regression)/(MS residual)
a 0.05, df = Numerator, Denominator, F Critical (from
the table) =
If F calculated >F Critical , H0 Rejected
Transcribed Image Text:Regression Steps STEP 1 PEARSON CORRELATION FIND r VALUE STEP 2 REGRESSION Regression function Σx ΣΥ = Σxy - ỹ = a + bx Σχ2ΣΥ2 : N = ExEy SP -Σxy - Slope b regression of line SP n (Ey)? b SSx SSy = Ey2 n (Σx)2 Y intercept a of regression line SSy Σχ2 а — Му — ьмх – bMx à = SP r = (SSx)(SSy) STEP 3 F RATIO HYPOTHESIS TESTING REGRESSIION STANDARD ERROR OF ESTIMATE STEP4 но- SS resi dual п — 2 SS regression =r2 SSy SS residual = (1-r^2 XSSY ) Df regression Df residual =n – 2 (Numerator) (denominator) MS regression = (SS regression)/df regression) MS residual = (SS residual)/(df residual) F= (MS regression)/(MS residual) a 0.05, df = Numerator, Denominator, F Critical (from the table) = If F calculated >F Critical , H0 Rejected
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