Question

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

x	y
81.1	86
77.5	60.4
92.7	126.5
104	132.5
85	53.1
64.3	95.5
64.6	31.7
39.7	5.7
82.3	121.3
82.4	98.2
29.2	-50.2
34.2	-1

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 87 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 =

Answer 1

The given data is inputted in EXCEL, post which the SCATTERPLOT function is used to obtain the scatter plot and then the TRENDLINE function is used to obtain the regression equation here as:

The correlation coefficient now is computed here as:

Therefore 0.903 is the required correlation coefficient here.

As the coefficient of determination here is 0.8156, therefore 81.56% of the variation in the in y can be explained by the variation in x here.

The regression equation can be seen from the plot here as:

Now the predicted value here is computed as:

Therefore 100.7 is the required predicted value here.