Problems 17–22 use the results from Problems 27–32 in Section ...

Question

Problems 17–22 use the results from Problems 27–32 in Section 4.1.

[DATA] Home Runs (Refer to Problem 31, Section 4.1.) The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game.

Table showing ball speed in mph and corresponding distance in feet for a sample of home runs.

b. Explain the meanings of the slope and y-intercept in this context, if appropriate.

Accepted Answer

Hello. In this video we are told that a health researcher studies the relationship between the average daily sleep duration in hours and the number of cups of coffee consumed per day among adults. The regression equation is y hat equal to -1.5 x plus 9. What does the slope and the intercept represent? So, let's go ahead and start this problem by first writing down the given regression equation. Now the given regression equation is Y equal to -1.5 x + 9. Now, the important thing to note here is that Y represents the daily sleep duration in hours, and X represents the number of coffee consumed per day among adults. Now, in order to interpret the slope and the Y intercept, let's go ahead and compare this to our traditional regression model. Now the traditional regression model is Y is equal to B + B1 X. Here bt represents the y intercept which is going to be the value of y when x is equal to 0. B1 represents the slope of the regression model, which is going to be the change in Y for every 1 unit change in X. So if we compare our given regression model to the traditional one, this will tell us that we are going to have a y intercept which is the constant value of 9. So b knot is equal to 9 in this case, and our slope is going to be the coefficient in front of the x variable, and that is going to be -1.5. Let's go ahead and start this problem by interpreting the Y intercept. Now again, the Y intercept is going to be the value of y when x is equal to 0, and since we have a Y intercept of 9, what this means is that we are going to have an average sleep duration of 9 hours with 0 cups of coffee. So we will have average sleep. Is 9 hours. With 0. Cups of coffee. This is going to be the interpretation of the y intercept for a regression model. Now let's go ahead and interpret the slope. Now there's one thing to note here, and it's that the slope is negative. Since we have a negative slope, this tells us that we are going to have an inverse relationship between the sleep duration and the number of cups of coffee. So what this tells us is that sleep duration should go down as coffee goes up, or the number of coffees goes down as sleep goes up. So what does this mean? Well, what this means is that the sleep duration. The sleep duration should decrease. By 1.5 hours. For every 1 cup Of coffee drink. And again, it will decrease 1.5 hours for every one cup of coffee, because this is going to be the change in Y for every one unit change in X. So this is going to be the interpretation of the slope and the white intercept for this problem. And with that being said, the correct solution to this problem should be option B. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Watch next