In: Advanced Math
Using your calculator, run a regression analysis on the following bivariate set of data with y as the response variable.
x y
71.2 23.1
90.8 122.9
88.8 82.9
57.7 18.3
71.4 8.6
60.4 25.9
60.2 -43.1
88.5 77.4
68.2 -5.9
41.1 -83
61.4 -2.5
87.1 39.4
Find the correlation coefficient and report it accurate to three decimal places. r =
What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.) r² = %
Based on the data, calculate the regression line (each value to three decimal places) y = x +
Predict what value (on average) for the response variable will be obtained from a value of 82.2 as the explanatory variable. Use a significance level of α = 0.05 to assess the strength of the linear correlation.
What is the predicted response value? (Report answer accurate to one decimal place.) y =
Proportion of the variation in y can be explained by the variation in the values of x = r2 = 0.8892 = 79.0%
Now,
The regression line is : - 202.205 + 3.177 X
Predicted response value = - 202.205 + 3.177*82.2 = 58.9
Significance of correlation coefficient :
The following needs to be tested:
Hence, Linear correlation is significant at 5% level of significance.