#### MS 150 Statistics Quiz 10: Linear regression revisited • Name:

Pixel versus hue angle data
PixelHue angle°
09
1517
3024
4524
6026
7530
9036
10543
12048
13552
15064
16577
18088
195111
210137
225165
240184
255200
270217
285230
300236
315239
330250
345270
360303

This section explores whether the hue angle changes linearly as one moves from red to magenta across a rainbow. The image of a rainbow was analyzed from red to purple. The hue angle for every 15th picture element (pixel) was measured and recorded. A spreadsheet with the data should be available at: http://www.comfsm.fm/~dleeling/statistics/s53/rainbow.xls

1. _________ Calculate the slope of the best fit (least squares) line for the data.
2. _________ Calculate the y-intercept of the best fit (least squares) line.
3. _________ Is the correlation positive, negative, or neutral?
4. _________ Use the equation of the best fit line to calculate the predicted hue angle for pixel 145.
5. _________ Use the inverse of the best fit line to calculate the predicted pixel for a hue angle of 220°.
6. _________ Calculate the linear correlation coefficient r for the data.
7. _________ Is the correlation none, low, moderate, high, or perfect?
8. _________ Calculate the coefficient of determination.
9. _________ What percent of the variation in the pixel data explains the variation in the hue angle data?
10. _________ Is there a relationship between the pixels and the hue angles?
11. _________ Can we use a linear regression to predict hue angles from pixels?
12.      Why or why not?
Linear Regression Statistics
Statistic or Parameter Symbol Equations Excel
Slope b   =SLOPE(y data, x data)
Intercept a   =INTERCEPT(y data, x data)
Correlation r   =CORREL(y data, x data)
Coefficient of Determination r2   =(CORREL(y data, x data))^2