Simple linear regression model

In summary, the conversation discusses two questions regarding the relationship between humidity and moisture content, and the interpretation of a regression slope in a given example. The first question is about the specific percentage increase in moisture content when humidity increases by 1 percent, while the second question is about rejecting the null hypothesis and concluding the value of the regression slope. It is recommended to refer to the original problem statement and final regression equation for a better understanding.
  • #1
tzx9633

Homework Statement


For the first question , why when the humidity increase by 1 percent , the moisture content will increase by 0.2727 percent ? Shouldn't it the moisture content will increase by 0.2727 + 0.4911 percent when the humidity increase by 1 percent ?
Second question , it's clear that in the 2nd photo , the slope , B_1 is 0.2724. It's is to test whether the slope equal to 1 in example 5 .. Why at the end of result , we should do not reject H0 , and conclude that B_1 is 1 ?
P/s : Example 5 (3rd and 4th photo) is continuous from example 3 (first and second photo)

Homework Equations

The Attempt at a Solution



I think for the second question is wrong . It's clear that in example 3 the B_1 is 0.2724 , which is not 1 . So , i think we should reject H0 , so that the slope , B_1 not equal to 1 . Correct me if i am wrong . [/B]
 

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  • #2
tzx9633 said:

Homework Statement


For the first question , why when the humidity increase by 1 percent , the moisture content will increase by 0.2727 percent ? Shouldn't it the moisture content will increase by 0.2727 + 0.4911 percent when the humidity increase by 1 percent ?
Second question , it's clear that in the 2nd photo , the slope , B_1 is 0.2724. It's is to test whether the slope equal to 1 in example 5 .. Why at the end of result , we should do not reject H0 , and conclude that B_1 is 1 ?
P/s : Example 5 (3rd and 4th photo) is continuous from example 3 (first and second photo)

Homework Equations

The Attempt at a Solution



I think for the second question is wrong . It's clear that in example 3 the B_1 is 0.2724 , which is not 1 . So , i think we should reject H0 , so that the slope , B_1 not equal to 1 . Correct me if i am wrong . [/B]

You should not expect helpers to look at your posted images. If you are serious about wanting help, you should type out the problem statement and the final regression equation. You can include the image of the data table---that is acceptable.

You should read the "pinned" thread "Guidelines for students and helpers" by Vela, to get a better idea of PF standards and recommendations.
 

1. What is a simple linear regression model?

A simple linear regression model is a statistical technique used to model the relationship between a single independent variable (X) and a continuous dependent variable (Y). It assumes that the relationship between X and Y can be represented by a straight line, with the goal of predicting the value of Y based on the value of X.

2. How is a simple linear regression model calculated?

To calculate a simple linear regression model, the following steps are typically taken:

  1. Collect a set of data points for both X and Y variables.
  2. Plot the data points on a scatter plot to visualize the relationship between the variables.
  3. Calculate the slope (β1) and intercept (β0) of the line of best fit using statistical techniques such as the least squares method.
  4. Use the equation Y = β0 + β1X to predict the value of Y for any given value of X.

3. What is the purpose of a simple linear regression model?

The purpose of a simple linear regression model is to understand and quantify the relationship between two variables. It can be used to make predictions about the value of the dependent variable based on the independent variable, and to identify any patterns or trends in the data.

4. What are the assumptions of a simple linear regression model?

The assumptions of a simple linear regression model include:

  • There is a linear relationship between the independent and dependent variables.
  • The data points are independent of each other.
  • The residuals (the differences between the observed and predicted values) are normally distributed.
  • The variability of the residuals is constant across all values of the independent variable.

5. What are the limitations of a simple linear regression model?

Some limitations of a simple linear regression model include:

  • It can only model the relationship between two variables.
  • If the relationship between the variables is not linear, the model may not accurately represent the data.
  • The model assumes that the data points are independent, which may not always be the case.
  • If there are outliers in the data, they can significantly affect the results of the model.

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