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4. 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 1 2 3 بن 4 10 5 6 7 8 9 10 School index z 9 5 7 6 4 9 7 8 5 6 House prices y 210 185 190 190 170 195 180 195 160 150 Σry = = 12,240, Στ’ = 462, Σy = 335,975 (a) (i) Construct a scatterplot of the data. (ii) Comment on the relationship between school quality index and house price. (b) A linear model of the form y = a + 3x + is fitted to the data, where the error terms (e) independently follow a N(0, 02) distribution with the variance o² being an unknown parameter. (i) Determine the fitted line of the regression model. (ii) Predict the average house price in Zambia when school index is 10. (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.

4. 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 1 2 3 بن 4 10 5 6 7 8 9 10 School index z 9 5 7 6 4 9 7 8 5 6 House prices y 210 185 190 190 170 195 180 195 160 150 Σry = = 12,240, Στ’ = 462, Σy = 335,975 (a) (i) Construct a scatterplot of the data. (ii) Comment on the relationship between school quality index and house price. (b) A linear model of the form y = a + 3x + is fitted to the data, where the error terms (e) independently follow a N(0, 02) distribution with the variance o² being an unknown parameter. (i) Determine the fitted line of the regression model. (ii) Predict the average house price in Zambia when school index is 10. (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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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4. 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 1 2 3 5 4 5 6 7 8 9 10 School index r 9 7 6 4 9 House prices y 210 185 190 190 170 195 180 195 160 150 7 8 5 Σry = 12,240, Σv2 = 462, Σy = 335,975 (a) (i) Construct a scatterplot of the data. (ii) Comment on the relationship between school quality index and house price. (b) A linear model of the form y = a + Br+ is fitted to the data, where the error terms (c) independently follow a N(0,02) distribution with the variance o² being an unknown parameter. (i) Determine the fitted line of the regression model. (ii) Predict the average house price in Zambia when school index is 10. (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) Dertemine 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.
Transcribed Image Text:4. 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 1 2 3 5 4 5 6 7 8 9 10 School index r 9 7 6 4 9 House prices y 210 185 190 190 170 195 180 195 160 150 7 8 5 Σry = 12,240, Σv2 = 462, Σy = 335,975 (a) (i) Construct a scatterplot of the data. (ii) Comment on the relationship between school quality index and house price. (b) A linear model of the form y = a + Br+ is fitted to the data, where the error terms (c) independently follow a N(0,02) distribution with the variance o² being an unknown parameter. (i) Determine the fitted line of the regression model. (ii) Predict the average house price in Zambia when school index is 10. (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) Dertemine 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.
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