Final answer:
The correct linear regression line for the dataset in question is ŷ = -173.51 + 4.83x, which indicates a moderate relationship with a correlation coefficient of 0.6631. Upon removing an outlier, the best fit line becomes ŷ = -355.19 + 7.39x with a stronger correlation coefficient of 0.9121, making it a better model for prediction.
Step-by-step explanation:
To import the timescore.csv file into RStudio, you can use the read.csv function. Once the data is imported, you can run a linear regression analysis to investigate if score (the dependent variable, usually denoted as y) is predicted by time (the independent variable, denoted as x).
To fit the linear regression model, you can use the lm function in R, which will give you the equation of the best fit line. The line is essentially an equation of the form: ý = a + bx. 'a' represents the y-intercept, and 'b' represents the slope of the line. This equation can be used to predict the value of y, given a value of x.
According to your information, the line of best fit is ý = -173.51 + 4.83x. To check if this regression line can be used for prediction, you should look at the correlation coefficient (r). If r is significantly different from zero, it suggests a significant linear relationship. In the provided dataset, with r = 0.6631, it indicates a moderate correlation. After an outlier is removed, the slope of the new best fit line is 7.39 with an increased r = 0.9121, implying a stronger linear relationship and a better predictive model.