From the following data, find the regression equation of Y on X and estimate Y when X = 10.

X	1	2	3	4	5	6
Y	2	4	7	6	5	6

Sum

From the table, we have

n = 6, ∑ x_i = 21, ∑ y_i = 30, `sum "x"_"i"^2 = 91`, ∑ x_i y_i = 116

`bar x = (sum x_i)/"n" = 21/6 = 3.5`

`bar y = (sum y_i)/"n" = 30/6 = 5`

Now, `"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`

`= (116 - 6xx3.5xx5)/(91 - 6(3.5)^2) = (116 - 105)/(91 - 73.5) = 11/17.5 = 0.63`

Also, `"a" = bar y - "b"_"YX" bar x`

= 5 - 0.63 × 3.5

= 5 - 2.205 = 2.8

The regression equation of Y on X is,

Y = a + b_YX X

∴ Y = 2.8 + 0.63 X

For X = 10,

Y = 2.8 + 0.63 × 10

= 2.8 + 6.3 = 9.1

∴ The value of Y when X =10 is 9.1

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Chapter 3: Linear Regression - Exercise 3.1 [Page 42]

Chapter 3 Linear Regression
Exercise 3.1 | Q 11 | Page 42

Choose the correct alternative:

There are ______ types of regression equations

Calculate the regression equations of X on Y and Y on X from the following data:

X	10	12	13	17	18
Y	5	6	7	9	13

The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.

Aptitude score (X)	60	62	65	70	72	48	53	73	65	82
Productivity Index (Y)	68	60	62	80	85	40	52	62	60	81

Obtain the two regression equations and estimate the test score when the productivity index is 75.

The following are the marks obtained by the students in Economics (X) and Mathematics (Y)

X	59	60	61	62	63
Y	78	82	82	79	81

Find the regression equation of Y on X.

From the following data obtain the equation of two regression lines:

X	6	2	10	4	8
Y	9	11	5	8	7

For the following data, find the regression line of Y on X

X	1	2	3
Y	2	1	6

Hence find the most likely value of y when x = 4.