Q.1 - Elementary Statistics

Question

1. For a linear equation $y=b_0+b_1{x}_{}$Identify the

a. independent variable.

b. dependent variable.

c. slope.

d. y-intercept.

Step-by-Step Solution

Answer

(a) $x$ is thus an independent variable.

(b)$y$ is thus a dependent variable.

(c) slope $=b_1$ 
(d) $y\text{ - intercept }=b_0$

Part (a)Step 1: Given information

Given in the question that,   We need to identify the independent variable for a linear equation  $y=b_0+b_1{x}_{}$ .

Part(a) Step 2: Explanation

$y=b_0+b_{1}x$is an equation.

Consider the formula  $y=b_0+b_{1}x$. 

No other variable influences the independent variable.

$x$ is thus an independent variable.

Part(b) Step 1: Given information

Given in the question that, We need to identify the dependent variable for a linear equation $y=b_0+b_{1}x$.

Part (b) Step 2: Explanation

 $y=b_0+b_{1}x$ is an equation.

Consider the formula $y=b_0+b_{1}x$

Any other variable influences the dependent variable.

The variable y is dependent on the variable $\mathrm{x}$, as shown in the previous equation.

$y$ is thus a dependent variable.

Part(c) Step 1: Given information

Given in the question that, We need to identify the  slope for a linear equation $y=b_0+b_{1}x$.

Part(c) Step 2: Explanation

The formula $y=b_0+b_{1}x$

Calculation:

Consider the formula $y=b_0+b_{1}x$.

Consider the following equation: $y=m x+c$

$m=b_1$ As a result, slope $=b_1$.

Part(d) Step 1: Given information

Given in the question that, We need to identify the  y-intercept for a linear equation $y=b_0+b_{1}x$

Part(d) Step 2: Explanation

$y=b_0+b_{1}x$ is an equation.

Consider the formula $y=b_0+b_{1}x$.

When the $x$ coordinate is equal to zero, the $y$ intercept of the above equation is produced.

$y=b_0+b_1\left(0\right)$

$y=b_0$

Hence,

$y\text{ - intercept }=b_0$