Mathematics: Which equation of the least squares regression line most closely matches the data set? note: the variable x represents the years after 1990. data set below x y 1990 45 1992 51 1994 57 1996 61 1998 75 1. y=5.5x+52 2. y=2.2x+13.8 3. y=3.5x+43.8 4. y=3.5x−43.8

10Step-by-step explanation:it takes 3/4 of a cup to make a mini loave of bread and 3/4 is about one cup so 10...

Which equation of the least squares regression

bigchungus69

17.01.2022

y = 3.5 x+ 43.8

Step-by-step explanation:

Here x represents the number of years after 1990

Thus, we get the table that is used to find the equation will be,

x 0 2 4 6 8

y 45 51 57 61 75

Let the equation that shows the above data,

y = b + a x ---------(1)

$\text{Where, }a=\frac{\sum y \sum x^2-\sum x \sum xy}{n(\sum x^2)-(\sum x)^2}$

$\text{And, }b = \frac{\sum xy - \sum x\sum y}{n\sum x^2 - (\sum x)^2}$

By the above table,

$\sum x = 20$

$\sum xy = 1296$

$\sum x^2 = 120$

$\sum y = 289$

By substituting these values in the above value of a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equation (1)

we get, the equation that shows the given data is,

y = 3.5 x + 43.8

⇒ Option (3) is correct.

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