Does IQ predict personal income? Measuring income in thousands of dol-lars, the following sample was collected pairing people’s IQ with their salaries:(106,56), (112,78), (81,47), (98,115) which produces a correlation coefficient ofr=0.303674 and standard deviations for X and Y:σX=13.45 andσY=30.2765 .a. Find the values ofaandbinˆY=a+bX(4 decimals). b. Find the residuals for all the data points. c. Predict the salary for a person with an IQ of 65 and for a person withan IQ of 130. 2. A particular athletic apparel store notices that among customers who pur-chase NFL jerseys from the store, just about 60% buy Colts jerseys, 30%buy Bears jerseys and 10% purchase another team. A randomly chosen sample of people who live near the store are asked abouttheir favorite teams, and the number of responses for the Colts was 27, forthe Bears was 17 and others was 6. Does the sample come from a population with the same distribution as thepeople who buy jerseys from this store? 3. A multiple regression has the formˆY=100+2.2X1−5.6X2a. Predict the response (Y) ifX1=15,X2=13 and ifX1=2,X2=4.b. Find the residual for (X1,X2,Y)=(15,13,90). 4. Identify any issues with Problem 1 and whyris so low.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Does IQ predict personal income? Measuring income in thousands of dol-lars, the following sample was collected pairing people’s IQ with their salaries:(106,56), (112,78), (81,47), (98,115) which produces a
.a. Find the values ofaandbinˆY=a+bX(4 decimals).
b. Find the residuals for all the data points.
c. Predict the salary for a person with an IQ of 65 and for a person withan IQ of 130.
2. A particular athletic apparel store notices that among customers who pur-chase NFL jerseys from the store, just about 60% buy Colts jerseys, 30%buy Bears jerseys and 10% purchase another team.
A randomly chosen sample of people who live near the store are asked abouttheir favorite teams, and the number of responses for the Colts was 27, forthe Bears was 17 and others was 6.
Does the sample come from a population with the same distribution as thepeople who buy jerseys from this store?
3. A multiple regression has the formˆY=100+2.2X1−5.6X2a. Predict the response (Y) ifX1=15,X2=13 and ifX1=2,X2=4.b. Find the residual for (X1,X2,Y)=(15,13,90).
4. Identify any issues with Problem 1 and whyris so low.
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