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# Statistics 359a - PowerPoint PPT Presentation

Statistics 359a. Regression Analysis. Necessary Background Knowledge - Statistics. expectations of sums variances of sums distributions of sums of normal random variables t distribution – assumptions and use calculation of confidence intervals simple tests of hypotheses and p-values.

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### Statistics 359a

Regression Analysis

• expectations of sums

• variances of sums

• distributions of sums of normal random variables

• t distribution – assumptions and use

• calculation of confidence intervals

• simple tests of hypotheses and p-values

• multiplication of conformable matrices

• transpose of a matrix

• determinant of a square matrix

• inverse of a square matrix

• eigenvalues of a square matrix

Introduction of the metric system and the length of a meter

• 1790 – French National Assembly commissions the French Academy of Sciences to design a simple decimal-based system of weights and measures

• 1791 – French Academy defines the meter to be 10-7 or one ten-millionth of the length of the meridian through Paris from the north pole to the equator.

• Legendre on the French commission in 1792 to determine the length of the meridian quadrant

• measurements of latitude made in 1795

• complex calculations made from the measurements in 1799

• Legendre proposes the method of least squares in 1805 to determine the length of a meter

• old French units of measurement: 1 module = 2 toises

• old French to imperial English: 1 toise = 6.395 feet

• metric to imperial: 1 meter = 3.2808 feet

D = 28497.78 modules

90D = 2564800.2 modules = length of the meridian quadrant

Therefore

1 meter = 0.256480 modules

= 0.512960 toises

= 3.280 feet

modern meter = 3.2808 feet

• Francis Galton, 1886, ‘Regression towards mediocrity in hereditary stature.’ Journal of the Anthropological Institute, 15: 246 – 263

• See JSTOR under UWO library databases

For X and Y bivariate normal with equal means variances

For  > 0

E(Y |X ) < x for x >  and

E(Y |X ) > x for x < 

• Relationship between the price of a violin bow and its attributes such as age, shape and ornamentation on the bow

• 1995 seems to be a more expensive year

• Is the effect confounded with some other attribute common to 1995?

• Is there anything special about 1920?

• Is there a quadratic trend in the data?

• Is there any trend with respect to the weight?

• No apparent trend

• The presence of gold on a bow generally makes it more expensive

• Some evidence of added expense for tortoise shell

• No apparent effect

Can we use the model built with the current data to predict the future price of a bow

Example: some 1999 data from auctions

1920 bow, 60.5 g., round with gold and pearl accessories - \$4098

1933 bow, 61 g., octagonal with pearl accessories only - \$2421

Prediction