Question

Given the following data: Year 1 2 3 4 5 Housing Starts (in Thousands) 3 6 2 5 4 Refrigerator Sales (in Millions) 6 7 4 10 8

Year	1	2	3	4	5
Housing Starts (in Thousands)	3	6	2	5	4
Refrigerator Sales (in Millions)	6	7	4	10	8

a) Use the Sum of Squares or Total Variation equation discussed in class to compute the Coefficient of Determination.

b) Interpret your answer in part(a).

Answer 1

The coefficient of determination is represented by R^2. This is calculated using the formula

R^2 = 1 – SSE/SST

SSE = sum of squares error = Summation (y - y_dash)^2

SST = sum of squares total = Summation (y - y_bar)^2

Here y_dash is the predicted value and y_bar is the mean value.

This equations are also mathematically (simplified) represented as shown below for R (coefficent of correlation) and we need to square it to obtain the value for R^2.a) The calculated values are shown below. The coefficient of determination (R^2) is 0.5b) The value of 0.5 means that 50% of the variance in refrigerator sales can be predicted by the housing start data. Overall the impact of fluctuation in the housing starts only contribute to 50% of the reason for fluctuation in refrigerator sales.