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?
a. the slope of the linear model is 0.01
b. the y-intercept of the linear model is 0.01
c. the x-intercept of the linear model is 0.01
d. the linear model is not a good fit
a correlation coefficient of absolute value close to one is a good fit. A correlation coefficient close to zero is a poor fit. 0.01 is a poor fit.
To answer this question, the student needs to understand the meaning of a correlation coefficient in the context of linear regression.
Correlation coefficient (or r-value) measures the strength and direction of the linear relationship between two variables. It can range from -1 to 1, where a value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no linear correlation.
In this case, the calculator gave a correlation coefficient of 0.01. Since it is very close to 0, it indicates a weak or negligible linear relationship between the variables.
Based on this information, the student can infer that the linear model is not a good fit for the data (option d). A correlation coefficient of 0.01 suggests that there is hardly any linear relationship between the dependent and independent variables.