Question

In: Statistics and Probability

Run a regression analysis on the following bivariate set of data with y as the response...

Run a regression analysis on the following bivariate set of data with y as the response variable.

x y
81 81.3
92.6 90.8
80.1 94.9
77.8 53.4
89.4 102.9
70.3 38.2
90.2 98
81.4 94.6
94.9 122.4
77.2 42.1
70.6 47.8
71 50.6

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 95.7 as the explanatory variable. Use a significance level of α=0.05α=0.05 to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)
y =

Solutions

Expert Solution

correlation coefficient r= Sxy/(√Sxx*Syy) = 0.881

r² = 0.881^2*100 = 77.7 %

3)

sample size n= 12
y̅ = 76.4167
x̅ = 81.3750
Sxx= Σ(Xi-X̅)2= 829.583
Sxy      =        Σ(Xi-X̅)(Yi-Y̅)= 2386.435
slope= β̂1 = Sxy/Sxx= 2.8767
intercept= β̂0 = y̅-β1x̅= -157.6723
Least square line equation: ŷ =2.877*x +(-157.672)

4)

predicted val=-157.672+95.7*2.877= 117.7 (please try 117.6 if this comes wrong)

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