It is thought that house prices in certain areas are correlated with the quality of schools

in the same areas. A study has been carried out in the ten provinces of Zambia where

average house prices (in thousands of dollars) and school quality indices ranging from 1

(very poor) to 10 (excellent) have been recorded:

Province 123 4 5 6 7 89 10

School index x 95 7 6 4 9 7 8 5 6

House prices y 210 185 190 190 170 195 180 195 160 150

xy = 12; 240,

x2 = 462,

y2 = 335; 975

(a) (i) Construct a scatterplot of the data.

(ii) Comment on the relationship between school quality index and house price.

(c) (i) Write down the ANOVA table.

(ii) Perform an F-test to test the null hypothesis that there is no linear relationship

between house prices and school indices, based on the ANOVA table.

(d) (i) Determine the percentage of variation in the average house prices in Zambia as

explained by school index.

(ii) Calculate the coefficient of correlation and give an interpretation.