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he values of x and their corresponding values of y are shown in the table below ...

Jul 4, 2024

he values of x and their corresponding values of y are shown in the table below x 0 1 2 3 4 y 2 3 5 4 6 Find the regression equation of the line y = a + bx b) Estimate the value of y when x = 10.

Solution by Steps

step 1

To find the regression equation of the line

y = a + bx

, we first need to perform a linear regression on the given data points:

(0, 2), (1, 3), (2, 5), (3, 4), (4, 6)

step 2

Using the Asksia-LL calculator, we input the data points and obtain the linear regression model:

y = 0.9x + 2.2

step 3

The regression equation is

y = 0.9x + 2.2

step 4

To estimate the value of

y

when

x = 10

, we substitute

x = 10

into the regression equation:

y = 0.9(10) + 2.2

step 5

Simplifying the expression:

y = 9 + 2.2 = 11.2

Answer

The regression equation is

y = 0.9x + 2.2

. When

x = 10

y

is estimated to be 11.2.

Key Concept

Linear Regression

Explanation

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.