HuskyGrad2010

A regression between the returns on a stock and its industry index returns gives the following results:

	Coefficient	Standard Error	t-value
Intercept	2.1	2.01	1.04
Industry Index	1.9	0.31	6.13

• The t-statistic critical value at the 0.01 level of significance is 2.58
• Standard error of estimate = 15.1
• Correlation coefficient = 0.849

The regression statistics presented indicate that the dispersion of stock returns about the regression line is:

A) 72.10.

B) 15.10.

C) 63.20.

---

The standard deviation of the differences between the actual observations and the projection of those observations (the regression line) is called the standard error of the estimate. The standard error of the estimate is the unsystematic risk.

HuskyGrad2010

The standard error of estimate is closest to the:

A) standard deviation of the independent variable.

B) standard deviation of the residuals.

C) standard deviation of the dependent variable.

---

The standard error of the estimate measures the uncertainty in the relationship between the actual and predicted values of the dependent variable. The differences between these values are called the residuals, and the standard error of the estimate helps gauge the fit of the regression line (the smaller the standard error of the estimate, the better the fit).

HuskyGrad2010

The standard error of the estimate measures the variability of the:

A) actual dependent variable values about the estimated regression line.

B) predicted y-values around the mean of the observed y-values.

C) values of the sample regression coefficient.

---

The standard error of the estimate (SEE) measures the uncertainty in the relationship between the independent and dependent variables and helps gauge the fit of the regression line (the smaller the standard error of the estimate, the better the fit).

Remember that the SEE is different from the sum of squared errors (SSE). SSE = the sum of (actual value - predicted value)2. SEE is the the square root of the SSE "standardized" by the degrees of freedom, or SEE = [SSE / (n - 2)]1/2

HuskyGrad2010

Jason Brock, CFA, is performing a regression analysis to identify and evaluate any relationship between the common stock of ABT Corp and the S&P 100 index. He utilizes monthly data from the past five years, and assumes that the sum of the squared errors is .0039. The calculated standard error of the estimate (SEE) is closest to:

A) 0.0082.

B) 0.0080.

C) 0.0360.

---

The standard error of estimate of a regression equation measures the degree of variability between the actual and estimated Y-values. The SEE may also be referred to as the standard error of the residual or the standard error of the regression. The SEE is equal to the square root of the mean squared error. Expressed in a formula,
SEE = √(SSE / (n-2)) = √(.0039 / (60-2)) = .0082

HuskyGrad2010

The standard error of the estimate in a regression is the standard deviation of the:

A) differences between the actual values of the dependent variable and the mean of the dependent variable.

B) residuals of the regression.

C) dependent variable.

---

The standard error is se = √[SSE/(n-2)]. It is the standard deviation of the residuals.

HuskyGrad2010

Which of the following statements about the standard error of the estimate (SEE) is least accurate?

A) The SEE will be high if the relationship between the independent and dependent variables is weak.

B) The SEE may be calculated from the sum of the squared errors and the number of observations.

C) The larger the SEE the larger the R2.

---

The R2, or coefficient of determination, is the percentage of variation in the dependent variable explained by the variation in the independent variable. A higher R2 means a better fit. The SEE is smaller when the fit is better.

HuskyGrad2010

If X and Y are perfectly correlated, regressing Y onto X will result in which of the following:

A) the standard error of estimate will be zero.

B) the regression line will be sloped upward.

C) the alpha coefficient will be zero.

---

If X and Y are perfectly correlated, all of the points will plot on the regression line, so the standard error of the estimate will be zero. Note that the sign of the correlation coefficient will indicate which way the regression line is pointing (there can be perfect negative correlation sloping downward as well as perfect positive correlation sloping upward). Alpha is the intercept and is not directly related to the correlation.

HuskyGrad2010

An analyst has been assigned the task of evaluating revenue growth for an online education provider company that specializes in training adult students. She has gathered information about student ages, number of courses offered to all students each year, years of experience, annual income and type of college degrees, if any. A regression of annual dollar revenue on the number of courses offered each year yields the results shown below.

Coefficient Estimates
Predictor	Coefficient	Standard Error of the Coefficient
Intercept	0.10	0.50
Slope (Number of Courses)	2.20	0.60

Which statement about the slope coefficient is most correct, assuming a 5% level of significance and 50 observations?

A) t-Statistic: 3.67. Slope: Not significantly different from zero.

B) t-Statistic: 3.67. Slope: Significantly different from zero.

C) t-Statistic: 0.20. Slope: Not significantly different from zero.

---

t = 2.20/0.60 = 3.67.  Since the t-statistic is larger than an assumed critical value of about 2.0, the slope coefficient is statistically significant.

HuskyGrad2010

Consider the regression results from the regression of Y against X for 50 observations:

Y = 0.78 + 1.2 X
The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45.

Which of the following reports the correct value of the t-statistic for the slope and correctly evaluates its statistical significance with 95% confidence?

A) t = 3.000; slope is significantly different from zero.

B) t = 1.789; slope is not significantly different from zero.

C) t = 2.667; slope is significantly different from zero.

---

Perform a t-test to determine whether the slope coefficient if different from zero. The test statistic is t = (1.2 – 0) / 0.45 = 2.667. The critical t-values for 48 degrees of freedom are ± 2.011. Therefore, the slope is different from zero.

HuskyGrad2010

Consider the regression results from the regression of Y against X for 50 observations:

Y = 0.78 - 1.5 X
The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45.

Which of the following reports the correct value of the t-statistic for the slope and correctly evaluates H0: b1 ≥ 0 versus Ha: b1 < 0 with 95% confidence?

A) t = -3.750; slope is significantly different from zero.

B) t = 3.750; slope is significantly different from zero.

C) t = -3.333; slope is significantly negative.

---

The test statistic is t = (-1.5 – 0) / 0.45 = -3.333. The critical t-value for 48 degrees of freedom is +/- 1.667. However, in the Schweser Notes you should use the closest degrees of freedom number of 40 df. which is +/-1.684. Therefore, the slope is different from zero. We reject the null in favor of the alternative.