Question: 52. Mandarin or Cantonese 2011 Below are data on Canadian cities, showing mother-tongue counts from the 2011 Census. a) Plot Cantonese speaker count versus Mandarin

52. Mandarin or Cantonese 2011 Below are data on Canadian cities, showing mother-tongue counts from the 2011 Census.

Urban Centre Abbotsford (BC) Barrie (ON) Cantonese Mandarin 310 400 215 295

Brantford (ON) 125 90 Calgary (AB) 20 175 11 380 Edmonton (AB)

a) Plot Cantonese speaker count versus Mandarin speaker count. Would you fit a regression line for predicting Cantonese speakers from Mandarin speakers? Explain.

b) Take the log (base 10) of both columns of numbers using your computer or calculator (why do you lose one city?). Now would you use regression for prediction purposes? What percentage of the variation in Cantonese counts is explained by the linear association with Mandarin counts? And stick to this log-log model for the remaining parts of this exercise.

c) Predict the Cantonese log count in a city where the Mandarin log count is 4.0. What would you predict for the actual Cantonese count?

d) What is the residual for the city of Vancouver?

e) Which city has the most surprising number of Cantonese speakers (considering the number of resident Mandarin speakers)? Give the residual.

f) Which cities have the greatest leverage on the fit?

Urban Centre Abbotsford (BC) Barrie (ON) Cantonese Mandarin 310 400 215 295 Brantford (ON) 125 90 Calgary (AB) 20 175 11 380 Edmonton (AB) 13 595 7295 Guelph (ON) 770 650 Halifax (NS) 460 805 Hamilton (ON) 1975 2215 Kelowna (BC) 235 210 Kingston (ON) 335 395 Kitchener-Cambridge- 1390 3 060 Waterloo (ON) London (ON) 1165 1415 Moncton (NB) 70 75 Montral (QC) 10 515 10 180 Oshawa (ON) Ottawa-Gatineau (ON-QC) 730 645 6 570 7275 Peterborough (ON) Qubec (QC) Regina (SK) 90 110 130 270 560 505 Saguenay (QC) Saint John (NB) 0 15 45 125 Saskatoon (SK) 865 790 Sherbrooke (QC) 20 65 St. Catharines-Niagara (ON) 640 555 St. John's (NL) 105 165

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