The Table Below Represents the Closing Prices of Stock ABC for the Last Five Days

Oct 13, 2025 by wbrum.org 111 views

The Table Below Represents the Closing Prices of Stock ABC for the Last Five Days

Introduction

Linear Regression Analysis is a statistical method used to establish a relationship between two variables. In this case, we are given the closing prices of stock ABC for the last five days, and we need to find the equation of linear regression that fits these data. The table below represents the closing prices of stock ABC for the last five days.

The Table Below Represents the Closing Prices of Stock ABC for the Last Five Days

Day	Value
1	100
2	110
3	120
4	130
5	140

Calculating the Linear Regression Equation

To calculate the linear regression equation, we need to follow these steps:

Calculate the mean of the x-values (Day): The mean of the x-values is calculated by adding up all the x-values and dividing by the number of data points.
Calculate the mean of the y-values (Value): The mean of the y-values is calculated by adding up all the y-values and dividing by the number of data points.
Calculate the deviations from the mean for the x-values: The deviations from the mean for the x-values are calculated by subtracting the mean of the x-values from each x-value.
Calculate the deviations from the mean for the y-values: The deviations from the mean for the y-values are calculated by subtracting the mean of the y-values from each y-value.
Calculate the slope (b1) of the linear regression line: The slope of the linear regression line is calculated using the formula:

b1 = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)²

where xi is the x-value, yi is the y-value, x̄ is the mean of the x-values, and ȳ is the mean of the y-values.

Calculate the intercept (b0) of the linear regression line: The intercept of the linear regression line is calculated using the formula:

b0 = ȳ - b1x̄

where b1 is the slope of the linear regression line, x̄ is the mean of the x-values, and ȳ is the mean of the y-values.

Calculating the Mean of the X-Values (Day)

The mean of the x-values is calculated by adding up all the x-values and dividing by the number of data points.

x̄ = (1 + 2 + 3 + 4 + 5) / 5 x̄ = 15 / 5 x̄ = 3

Calculating the Mean of the Y-Values (Value)

The mean of the y-values is calculated by adding up all the y-values and dividing by the number of data points.

ȳ = (100 + 110 + 120 + 130 + 140) / 5 ȳ = 600 / 5 ȳ = 120

Calculating the Deviations from the Mean for the X-Values

The deviations from the mean for the x-values are calculated by subtracting the mean of the x-values from each x-value.

Day	Deviation from Mean
1	1 - 3 = -2
2	2 - 3 = -1
3	3 - 3 = 0
4	4 - 3 = 1
5	5 - 3 = 2

Calculating the Deviations from the Mean for the Y-Values

The deviations from the mean for the y-values are calculated by subtracting the mean of the y-values from each y-value.

Day	Value	Deviation from Mean
1	100	100 - 120 = -20
2	110	110 - 120 = -10
3	120	120 - 120 = 0
4	130	130 - 120 = 10
5	140	140 - 120 = 20

Calculating the Slope (b1) of the Linear Regression Line

The slope of the linear regression line is calculated using the formula:

b1 = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)²

where xi is the x-value, yi is the y-value, x̄ is the mean of the x-values, and ȳ is the mean of the y-values.

b1 = [(-2)(-20) + (-1)(-10) + (0)(0) + (1)(10) + (2)(20)] / [(-2)² + (-1)² + (0)² + (1)² + (2)²] b1 = [40 + 10 + 0 + 10 + 40] / [4 + 1 + 0 + 1 + 4] b1 = 100 / 10 b1 = 10

Calculating the Intercept (b0) of the Linear Regression Line

The intercept of the linear regression line is calculated using the formula:

b0 = ȳ - b1x̄

where b1 is the slope of the linear regression line, x̄ is the mean of the x-values, and ȳ is the mean of the y-values.

b0 = 120 - (10)(3) b0 = 120 - 30 b0 = 90

The Equation of Linear Regression

The equation of linear regression is given by:

y = b0 + b1x

where b0 is the intercept, b1 is the slope, x is the independent variable, and y is the dependent variable.

y = 90 + 10x

This is the equation of linear regression that fits the data.

Conclusion

In this article, we have calculated the equation of linear regression that fits the closing prices of stock ABC for the last five days. The equation of linear regression is given by:

y = 90 + 10x

This equation can be used to predict the closing prices of stock ABC for future days.
Frequently Asked Questions (FAQs) About Linear Regression

Introduction

Linear regression is a statistical method used to establish a relationship between two variables. In this article, we have calculated the equation of linear regression that fits the closing prices of stock ABC for the last five days. Here are some frequently asked questions (FAQs) about linear regression:

Q: What is linear regression?

A: Linear regression is a statistical method used to establish a relationship between two variables. It is a type of regression analysis that assumes a linear relationship between the independent variable (x) and the dependent variable (y).

Q: What is the equation of linear regression?

A: The equation of linear regression is given by:

y = b0 + b1x

where b0 is the intercept, b1 is the slope, x is the independent variable, and y is the dependent variable.

Q: How do I calculate the equation of linear regression?

A: To calculate the equation of linear regression, you need to follow these steps:

Calculate the mean of the x-values (independent variable).
Calculate the mean of the y-values (dependent variable).
Calculate the deviations from the mean for the x-values.
Calculate the deviations from the mean for the y-values.
Calculate the slope (b1) of the linear regression line.
Calculate the intercept (b0) of the linear regression line.

Q: What is the slope (b1) of the linear regression line?

A: The slope of the linear regression line is a measure of the change in the dependent variable (y) for a one-unit change in the independent variable (x). It is calculated using the formula:

b1 = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)²

where xi is the x-value, yi is the y-value, x̄ is the mean of the x-values, and ȳ is the mean of the y-values.

Q: What is the intercept (b0) of the linear regression line?

A: The intercept of the linear regression line is the value of the dependent variable (y) when the independent variable (x) is equal to zero. It is calculated using the formula:

b0 = ȳ - b1x̄

where b1 is the slope of the linear regression line, x̄ is the mean of the x-values, and ȳ is the mean of the y-values.

Q: What is the purpose of linear regression?

A: The purpose of linear regression is to establish a relationship between two variables and to make predictions about the dependent variable based on the independent variable.

Q: What are the assumptions of linear regression?

A: The assumptions of linear regression are:

Linearity: The relationship between the independent variable (x) and the dependent variable (y) is linear.
Independence: The observations are independent of each other.
Homoscedasticity: The variance of the residuals is constant across all levels of the independent variable.
Normality: The residuals are normally distributed.
No multicollinearity: The independent variables are not highly correlated with each other.

Q: What are the limitations of linear regression?

A: The limitations of linear regression are:

It assumes a linear relationship between the independent variable (x) and the dependent variable (y).
It assumes that the residuals are normally distributed.
It assumes that the variance of the residuals is constant across all levels of the independent variable.
It assumes that the observations are independent of each other.

Q: What are the applications of linear regression?

A: The applications of linear regression are:

Predicting the value of a dependent variable based on the value of an independent variable.
Establishing a relationship between two variables.
Identifying the factors that affect a dependent variable.
Making predictions about the future values of a dependent variable.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) about linear regression. Linear regression is a statistical method used to establish a relationship between two variables and to make predictions about the dependent variable based on the independent variable. It assumes a linear relationship between the independent variable (x) and the dependent variable (y) and has several assumptions and limitations.