A sudent is analyzing data from an experiment using a linear model. when the student entered the data into his calculator and ran a least squares linear regression the calculator gave a correlation coefficient of 0.01. what can the student infer from this coefficient?
1. the slope of the linear model is 0.01
2. the y-intercept of the linear model is 0.01
3. the x-intercept of the linear model is 0.01
4. the linear model is not a good fit
To understand what the correlation coefficient of 0.01 implies, let's first discuss what a correlation coefficient represents. The correlation coefficient is a statistical measure that indicates the strength and direction of the linear relationship between two variables. It ranges from -1 to 1.
In this case, a correlation coefficient of 0.01 suggests a very weak or almost no linear relationship between the variables in the dataset. The closer the correlation coefficient is to zero, the weaker the relationship is.
Now, let's analyze each statement provided:
1. The slope of the linear model is 0.01: The correlation coefficient does not directly provide information about the slope of the linear model. Therefore, we cannot infer this from the given correlation coefficient.
2. The y-intercept of the linear model is 0.01: The correlation coefficient does not provide any information about the y-intercept either. Hence, this cannot be inferred from the correlation coefficient.
3. The x-intercept of the linear model is 0.01: Similarly, the correlation coefficient does not provide information about the x-intercept of the linear model. Therefore, this inference is also not valid.
4. The linear model is not a good fit: This inference is valid because a correlation coefficient of 0.01 indicates a very weak linear relationship between the variables. It suggests that the linear model does not adequately explain the relationship between the variables in the dataset. Generally, correlation coefficients below 0.3 are considered weak, and this particular coefficient falls within that range.
In summary, the correct inference from a correlation coefficient of 0.01 is that the linear model is not a good fit for the data.
The student can infer that:
4. The linear model is not a good fit.
A correlation coefficient of 0.01 indicates a very weak linear relationship between the variables being analyzed. In other words, the variables have very little or no linear association. Therefore, the linear model is not a good fit for the data.