Chapter 4: Q.4.52 (page 174)

a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain $s_{x x} a n d s_{x y}$
b. Graph the regression equation and the data points

Short Answer

Expert verified

(a) $\hat{y} = 14 - 3 x$

(b)

Step by step solution

Part(a) Step 1:Given Information

The given data is:

We have to determine the regression equation.

Part (a) Step 2: Explanation

The variables $b_{0}$ and $b_{1}$ are used to create the regression equation. For a collection of $n$ data points, the regression equation is

$\hat{y} = b_{0} + b_{1} x$

Where,

$b_{0} = y - b_{1} x$

$b_{1} = \frac{s_{x y}}{s_{x x}}$

The table can be obtained as:

$s_{x x} = 9$

$s_{x y} = 18$

Therefore,

$b_{1} = - 0.5$

$b_{0} = 14$

Therefore, the regression equation will be ,

$\hat{y} = 14 - 3 x$

Part (b) Step 1 :Given Information

The given data is:

We have to determine the graph of regression equation and data points.

Part (b) Step 2: Explanation

The regression equation and data points can be drawn on graph as:

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a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain $s_{x x} a n d s_{x y}$
b. Graph the regression equation and the data points

Short Answer

Step by step solution

Part(a) Step 1:Given Information

Part (a) Step 2: Explanation

Part (b) Step 1 :Given Information

Part (b) Step 2: Explanation

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a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain sxxandsxyb. Graph the regression equation and the data points

Short Answer

Step by step solution

Part(a) Step 1:Given Information

Part (a) Step 2: Explanation

Part (b) Step 1 :Given Information

Part (b) Step 2: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain $s_{x x} a n d s_{x y}$
b. Graph the regression equation and the data points