# A sample of x and y scores is taken, and a regression line is used to predict y from x. if ssy’ =300, sse=500, and n=50, what is s

Question

A sample of x and y scores is taken, and a regression line is used to predict y from x. if ssy’ =300, sse=500, and n=50, what is ssy?

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1 month 2022-12-31T03:05:50+00:00 2 Answers 0 views 0

1. The value of SSY (the sum of squares Y) is 800 for the given regression line.
We know that:
SSY – the sum of squares Y – which can be partitioned into two parts:
1) SSY’ –  the sum of squares predicted
2) SSE – the sum of squares error.
The sum of squares predicted means that:
The sum of  squared deviations of the predicted scores that from the mean predicted score.
We have:
A sample of X and Y scores, a regression line to predict Y from X.
SSY¹ = 300
SSE = 500
n = 50
Now, we know that:
SSY = SSY¹ + SSE
SSY = 500 + 300
SSY = 800
Therefore, the value of SSY (the sum of squares Y) is 800.
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2. The value of SSY (the sum of squares Y) is 800.

### Partitioning the Sums of Squares in Regression

SSY – the sum of squares Y can be partitioned into two parts:
SSY’ –  the sum of squares predicted
SSE – the sum of squares error.
The sum of squares predicted is the sum of the squared deviations of the predicted scores from the mean predicted score.

### What do you meant by Regression Line ?

A regression line is an estimate of the line that describes the true, but unknown, linear relationship between the two variables. The equation of the regression line is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.
Here, we have given that:
A sample of X and Y scores is taken, and a regression on line is used to predict Y from X.
if SSY¹ = 300
SSE = 500
n = 50
we know,
SSY = SSY¹ + SSE
SSY = 500 + 300
SSY = 800
Hence,
The value of SSY (the sum of squares Y) is 800.