Final answer:
In R, a linear regression analysis is performed using the lm() function, and R-squared is interpreted as the proportion of variance in the dependent variable explained by the independent variable.
Step-by-step explanation:
To perform a linear regression analysis in R with fare as the dependent variable and distance as the independent variable, you would use the lm() function in R to fit the model, then summary() to display the results which will include the R-squared value. The R-squared value indicates how much of the variability in the fare can be explained by the distance traveled. A higher R-squared value means the model explains a higher proportion of the variation.
To interpret the model's R-squared value, if the R-squared value is, for instance, 0.75, this means that 75% of the variance in fare can be explained by the distance traveled. The remaining 25% of the variance is due to other factors not included in the model. This percentage can be calculated using the formula r² = r * r where r is the correlation coefficient.