handout_2_3 - 2.3 Least-Squares Regression correlation...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
2.3 Least-Squares Regression correlation measures the direction and strength of the linear relationship between two quantitative variables we would like to summarize the overall pattern by drawing a line on the scatterplot A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x. Regression, unlike correlation, requires that we have an explanatory variable and a response variable. Example Does fidgeting keep you slim? Some people don’t gain weight even when they overeat. Perhaps fidgeting and other “nonexercise activity” (NEA) explains why- the body might spontaneously increase NEA when fed more. Researchers deliberately overfed 16 healthy adults for 8 weeks. The measured fat gain (response variable) and the increase in NEA (explanatory variable). Here are the data: NEA increase (calories)- X Fat gain (kg)- Y -94 4.2 -57 3.0 -29 3.7 135 2.7 143 3.2 151 3.6 245 2.4 355 1.3 392 3.8 473 1.7 486 1.6 535 2.2 571 1.0 580 0.4 620 2.3 690 1.1 Figure 2.11 displays the scatterplot (response-y, explanatory-x) we can describe the overall pattern by drawing a straight line through the points no straight line passes exactly through all the points fitting a line to data means drawing a line that comes as close as possible to the points
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Straight Lines Suppose that y is a response variable (vertical axis) and x is an explanatory variable (horizontal axis). A straight line relating y to x has an equation of the form: y = a + bx In this equation, b is the slope, the amount by which y changes when x increases by one unit. The number a is the intercept, the value of y when x=0. Any straight line describing our data has the form: fat gain = a + (b * NEA increase) Figure 2.12 The computer generates the following regression line: fat gain = 3.505 - (0.00344 * NEA increase) slope b = -0.00344 tells us that fat gained goes down by 0.00344 kg for each calorie increase in NEA slope b tells us rate of change in response variable (y) as explanatory variable (x) changes intercept a = 3.505 kg is the estimated fat gain if NEA does not change when a person overeats Prediction #1) Suppose an individual’s NEA increase when overeating is 400 calories.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern