A company's investment is widely believed to be a function of interest rate. To estimate this relationship, a professor randomly selected 20 of companies in the market and collected information on their investment (Y, in millionss) and interest rate (X) patterns. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 15.50 and the slope = -0.46. Also, the sum of squares total (SST) and the regression sum of squares (SSR) were equal to 46980.74 and 32831.23, respectively. Based on this information, the standard error of the estimate is equal to __________. Round your final answer to two decimal places.
Question
A company's investment is widely believed to be a function of interest rate. To estimate this relationship, a professor randomly selected 20 of companies in the market and collected information on their investment (Y, in millionss) and interest rate (X) patterns. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 15.50 and the slope = -0.46. Also, the sum of squares total (SST) and the regression sum of squares (SSR) were equal to 46980.74 and 32831.23, respectively. Based on this information, the standard error of the estimate is equal to __________. Round your final answer to two decimal places.
Solution
To calculate the standard error of the estimate, we first need to calculate the residual sum of squares (SSE). The formula for SSE is:
SSE = SST - SSR
Substituting the given values:
SSE = 46980.74 - 32831.23 = 14149.51
Next, we calculate the degrees of freedom, which is the number of observations minus the number of parameters estimated from the data. In this case, we have estimated two parameters (the intercept and the slope), so the degrees of freedom is:
df = n - 2 = 20 - 2 = 18
Now we can calculate the standard error of the estimate, which is the square root of the SSE divided by the degrees of freedom. So:
Standard error = sqrt(SSE/df) = sqrt(14149.51/18)
Calculating this gives a standard error of approximately 28.07 when rounded to two decimal places.
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Determination of interest rates
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