Regression lesson 4 Starter Dangers of Predicting (extrapolation) Interpretation questions Exam questions.

Example: The table shows the latitude, x, and mean January temperature(°C), y, for a sample of 10 cities in the northern hemisphere. Calculate the equation of the regression line of y on x and use it to predict the mean January temperature for the city of Los Angeles, which has a latitude of 34°N. Regression CityLatitudeMean Jan. temp. (°C) Belgrade451 Bangkok1432 Cairo3014 Dublin503 Havana2322 Kuala Lumpur327 Madrid405 New York410 Reykjavik30–1 Tokyo365 Response variable y Explanatory variable x

Using a calculator gives A = , B = This is our estimate of the mean January temperature in Los Angeles Regression So, when x = 34, y = 33.3 – × 34 = 8.82°C. Note: This prediction for the mean January temperature in Los Angeles is based purely on the city’s latitude and takes no account of additional factors that can affect the climate of a city, such as altitude or proximity to the coast This gives y = 33.3 – 0.720x

Regression d1d1 d2d2 d3d3 d4d4 d5d5 d6d6 The distances d i are referred to as residuals Note: The best fitting line should pass through the mean point,. The best fitting line is the one that minimizes the sum of the squared deviations,, where d i is the vertical distance between the i th point and the line.

A regression equation can only confidently be used to predict values of y that correspond to x values that lie within the range of the data values available. Dangers of Predicting (extrapolation) It can be dangerous to extrapolate (i.e. to predict) from the graph, a value for y that corresponds to a value of x that lies beyond the range of the values in the data set. It is reasonably safe to make predictions within the range of the data. It is unwise to extrapolate beyond the given data. This is because we cannot be sure that the relationship between the two variables will continue to be true.

Interpretation of A and B for starter Give an interpretation of A and B in context Using a calculator gives A = , B = Latitude Mean temperature A is the temperature when latitude is 0 ie the temperature at the equator B is the decrease in temperature per increase in one degree of latitude.

Interpretation questions from booklet

Exam questions in booklet