{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

17 Regression - Regression Predicts Y from X Linear...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Regression ! Predicts Y from X ! Linear regression assumes that the relationship between X and Y can be described by a line Correlation vs. regression Regression assumes... ! Random sample ! Y is normally distributed with equal variance for all values of X The parameters of linear regression Y = ! + X
Image of page 1

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

View Full Document Right Arrow Icon
Positive ! Negative ! ! = 0 Higher Lower Estimating a regression line Y = a + b X Nomenclature Residual: Y i ! ˆ Y i Finding the "least squares" regression line SS residual = Y i ! ˆ Y i ( ) 2 i = 1 n Minimize:
Image of page 2
Best estimate of the slope b = X i ! X ( ) Y i ! Y ( ) i = 1 n X i ! X ( ) 2 i = 1 n (= "Sum of cross products" over "Sum of squares of X") Remember the shortcuts: X i ! X ( ) Y i ! Y ( ) i = 1 n " = X i Y i " # $ % % & ( ( ! X i Y i " " n X i ! X ( ) 2 i = 1 n " = X i 2 ( ) " ! X i " # $ % % & ( ( 2 n Finding a Y = a + b X So.. a = Y ! b X Example: Predicting age based on radioactivity in teeth Many above ground nuclear bomb tests in the ‘50s and ’60s may have left a radioactive signal in developing teeth. Is it possible to predict a person’s age based on dental C 14 ?
Image of page 3

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

View Full Document Right Arrow Icon
Teeth data: Estimated Actual 1982 1985 1985 1986 1987 1987 1990 1989 1991 1991 1991 1991 1992 1991 1954 1951 1956 1951 1954 1958 Estimated Actual 1963 1963 1963 1964 1965 1964 1967 1970 1969 1972 1970 1973 1973 1972 1974 1975 1980 1983 1982 1983 Teeth data: X = 39488, Y ! !
Image of page 4
Image of page 5
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