Report the r^2 linear correlation coefficient and the linear regression equation
ID: 3236123 • Letter: R
Question
Report the r^2 linear correlation coefficient and the linear regression equation produced in the Excel spreadsheet. What would be the value of Pearson's r (simply the squareroot of r^2)? Would Pearson's r be positive or negative? What does this imply about the relationship between the factors in this study? What is the implication of any correlation found between the variables in the study you picked? Does this correlation imply a causal relationship? Explain. Are there other variables that you think should have been examined that would have improved this study or helped to pinpoint what factors are causal?Explanation / Answer
2) In excel spreadsheet , we input the values
Using Intercept formula we get intercept as 59.4135 and using Slope formula in excel we get Slope as 1.3806.
Therefore regression equation is y=59.4135 + 1.3806x .
Correlation can be found by using Correl formula in excel and it r2 = 0.83202 .
3) Pearson's r = Squareroot of (0.83202) = 0.912151
4) Pearson's r can be positive and negative too , it ranges from (-1,1) . In this study it is 0.912151 indicates strong association between x and y variables in this study.
5) There is a strong correlation between these variables as r2 value is 0.83202 which is close to 1 and also r value is 0.912151 which is close to 1 indicating a very strong relationship between variables.
6) Yes. This indicates a causal relationship between independent and dependent variable . i.e x independent variable increases y dependent variable increases by 1.38. So there is positive dependency between x and y variable.
7) No. To check dependency between x and y variables this check is sufficient.
x values y values 12 74 14 75 17 78 21 91.5 20 94 25 97 22 93 24 89 19 90 26 88 27 95 18.5 84 25.5 94 19.6 90.5