Is this graph linear?
Answer (1)
Solution ProcessTo determine if the graph is linear, we need to consider the following:1. Visual InspectionThe data points appear to generally follow a downward trend, which suggests a possible linear relationship. However, visual inspection alone can be misleading.2. Best Fit Line EquationThe equation of the best fit line is given as [tex]$y = -0.0134x + 0.016...$[/tex]. This is a linear equation (of the form [tex]$y = mx + b$[/tex]), which suggests a linear relationship.3. R-squared ValueThe R-squared value ([tex]$R^2$[/tex]) is 0.9133. The R-squared value represents the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x). An [tex]$R^2$[/tex] value close to 1 indicates that the model fits the data well, suggesting a strong linear relationship. In this case, 0.9133 is relatively close to 1, indicating a good fit.[tex]\\[/tex]Final answer:Based on the best fit line equation and the R-squared value, the graph can be considered approximately linear. The $R^2$ value of 0.9133 indicates that the linear model explains a large portion of the variance in the data.Therefore, yes, the graph is approximately linear.
