STA404 Slides Lectures 1-15 by Mahar Afaq

How to fit a Regression line?

Procedure and step by step

calculation with example

STA404

Lesson 1

How to fit a Regression line?

Example:

The following table describes data for the number of people using a swimming pool over 8 days in summer and the corresponding maximum temperature (in degrees Celsius) on each day.

Day · Temperature (0C) · x · Number of people y · Equation of Regression line · ˆy · a · b x

Formula forb

n xy x y b n x x Formula fora

a y b x

n

xy

x

y

x x

y

a y b x n xy x y b n x x

Required Calculation

Day X Y XY X2 Y2

5600 78400

8640 129600

16200 1296 202500

13440 1024 176400

11200 160000

19000 1444 250000

16150 1156 225625

8320 102400

Total · 3205 · 98550 · 7356 · 1324925

– From previous table we have:

– Now putting these values in “b” and “a”, and by solving,

we get:

8( (238)(3205) 25610 11.62 8( (238) 98550 n xy x y b n x x

400.62 11.62(29.75) 54.92 a y b x 3205

7356

98550 n

x

y

x

xy 3205 400.62

29.75 y y n x x n

• Putting the values of “a” and “b” in the equation,

we get:

– Interpretation:

• This means that if the daily temperature is

increased by 1 degree, we would expect the 11.62

more person to use the swimming pool. No. of Peop ˆy 54.92 11.62(x)

54.92 11.62 (Temp l rature) e

What is Coefficient of

Determination?

SST, SSE, SSR and CoD with example

and explanation STA404

Lesson 3

Topic

 What is SSE?

 What is SSR?

 What is SST?

 What is Coefficient of Determination?

Example · Tip for Service · Tip for Service · Tip for Service · Residuals · Squaring the Residuals (Errors)