Our dataset contains the following variables:

Year:the year of the Olympic Games, from 1896 to 2016.

Time:the winning time for the 1,500 meter race, in seconds.

First, let's explore the relationship between the two quantitative variablesyear and time. Produce a scatterplot and use it to verify that year and time are nearly linear in their relationship.Observe that the form of the relationship between the 1,500 meter race's winning time and the year is linear. The least squares regression line is therefore an appropriate way to summarize the relationship and examine the change in winning times over the course of the last century. We will now find the least squares regression line and plot it on a scatterplot.

Include the scatterplotwith the regression lineand correlation coefficient in your MS Word Document.

a.Give the equation for the least squares regression line.

b.What is the slope and interpret it in this context?

c.Interpret the correlation coefficient for strength and direction.

Question 2:

Remove any outlier(s) from the data set by deleting both the year and time.Repeat the steps from Question 1 and include the newscatterplot and correlation coefficient in your MS Word Document.

a.Give the equation for this new regression line.

b.Interpret the correlation coefficient for strength and direction.

c.What effect does removing the outlier(s) have on the strength of the correlation in the scatterplot?

Question 3:

Our least squares regression line associates years as an explanatory variable, with times in the race as the response variable.

a.Use the least squares regression line you found in question 2 to predict the race time in the 2016 Olympic Games.Hint: Year is the explanatory variable.

b.How does the prediction compare with the actual time?

c.Give a reason as to why it does or why it does not match the 2016 Olympic Games time? (Just curious as to your speculation.No right or wrong answers here.