1.) You compare the height and weight of 5 adult women. You get the following results: height 60 67 62 70 66 weight 119 143 131 155 136 1A.) Construct a scatter plot of height (x) vs. weight (y) 1B.) Calculate the following (show your work for SScp): SSx SSy SScp ̄x ̄y 1C.) Calculate the correlation coefficient (r) 2.) Use the information from problem 1. Perform a complete test of the hypothesis that the population correlation coefficient (ρ) is 0. Show all steps (note - obviously this should be a one sided test! Make sure you know why!). 3.) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data from problem (1) and do a regression instead. 3A.) Calculate b0 and b1. 3B.) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just “sketch”, be a little careful). 4(a) Now do a significance test of H0: β1 = 0. Show all your calculations (including your residual calculations). Again, note that this should be a one sided test (why?). 4(b) Compare your t* from 4(a) with your t* from problem 2. Are they the same? This is not a coincidence, although once you do more complicated analyses, you can't rely on this “equivalence”.
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.
1.) You compare the height and weight of 5 adult women. You get the following results:
|
height |
60 |
67 |
62 |
70 |
66 |
|
weight |
119 |
143 |
131 |
155 |
136 |
1A.) Construct a
1B.) Calculate the following (show your work for SScp):
SSx SSy SScp ̄x ̄y
1C.) Calculate the
2.) Use the information from problem 1. Perform a complete test of the hypothesis that the population correlation coefficient (ρ) is 0. Show all steps (note - obviously this should be a one sided test! Make sure you know why!).
3.) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data from problem (1) and do a regression instead.
3A.) Calculate b0 and b1.
3B.) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just “sketch”, be a little careful).
4(a) Now do a significance test of H0: β1 = 0. Show all your calculations (including your residual calculations). Again, note that this should be a one sided test (why?).
4(b) Compare your t* from 4(a) with your t* from problem 2. Are they the same? This is not a coincidence, although once you do more complicated analyses, you can't rely on this “equivalence”.
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