# STAT 1430 Lecture Notes - Lecture 6: Pearson Product-Moment Correlation Coefficient, Descriptive Statistics, Regression Analysis

STAT1430.01–Lecture6–Correlation and Regression Jan 24, 2019

•Criteria for Best Line: Smallest SSE

oSSE= Sum of the square for error

oFind the line with the smallest SSE, from all the potential lines that go through

the data.

oIn the equation , find the values of and that minimize SSE.

oFrom this and you create the “least squares regression line.”

•Picture of Minimizing SSE

o

oMany Possible Lines

oTake the one with the smallest (“least”) SSE

•Coefficients of the least squares (best fitting) regression line

oBest line is

oBest slope is = r *

▪Here we need r, ,

oBest y-intercept is

▪Here we need , after is computed, only to 5 numbers find best fit

•Find the coefficients using descriptive statistics: Football Data

oDescriptive statistics: Temperature, Coffees

oCorrelations: Temperature, Coffees

oPearson correlation of Temperature and Coffees = r = -0.741

oP-Value = 0.000

̂

y=b0+b1x

b0

b1

b0

b1

̂

y=b0+b1x

b1

Sy

Sx

Sy

Sx

b0= ¯y−b1¯x

¯x

¯y

b1

Variable

Mean

Standard Deviation

Te m p e r a t u r e

35.08

16.29

Coffees

29913

12174

## Document Summary

Criteria for best line: smallest sse: sse= sum of the square for error, find the line with the smallest sse, from all the potential lines that go through the data, in the equation. , find the values of b0 and b1 that minimize sse: from this b0 and b1 you create the least squares regression line. Picture of minimizing sse: many possible lines, take the one with the smallest ( least ) sse. Coefficients of the least squares (best fitting) regression line: best line is. Y = b0 + b1x: best slope is = r * b1. Sy sx: here we need r, , best y-intercept is b0 = y b1 x, here we need , after. X y b1 is computed, only to 5 numbers find best fit. Find the coefficients using descriptive statistics: football data: descriptive statistics: temperature, coffees. 12174: correlations: temperature, coffees, pearson correlation of temperature and coffees = r = -0. 741, p-value = 0. 000.