1. The following data show the results of an aptitude test (Y) and the grade point average of 10 students. Aptitude Test Score (Y) GPA (X) 26 1.8 31 2.3 28 2.6 30 2.4 34 2.8 38 3.0 41 3.4 44 3.2 40 3.6 43 3.8 a. Develop a least squares estimated regression line. (5%) b. Compute the coefficient of determination and comment on the strength of the regression relationship. (5%) c. Is the slope significant? Use a t test and let a = 0.05. (5%) d. At 95% confidence, test to determine if the model is significant (i.e., perform an F test). (5%) 2. Shown below is a portion of a computer output for a regression analysis relating Y (dependent variable) and X (independent variable). Predictor Coefficient Standard Error Constant 16.156 1.42 X -0.903 0.26 ANALYSIS OF VARIANCE SOURCE SS DF Regression 50.58 1 Error 55.42 13 a. Perform a t-test and determine whether or not demand and unit price are related. Let = 0.05. (10%) b. Compute the coefficient of determination and fully interpret the meaning. Be very specific. (10%) 3. In order to determine the relationship between the price of an item (X) and the quantity sold (Y), the price of the item was varied over 10 consecutive days. The following data are the results of the study. X = 60, X2 = 436, Y = 63, Y2 = 469, XY = 335, SSR = 24.3289 a. Develop the least squares estimated regression line. (6%) b. Calculate SSE. c. Perform a t test and determine whether or not the slope is significantly different from zero. Let = 0.05. (6%) d. At = 0.05, perform an F test to determine if the regression model is significant. (6%) e. Develop a 90% confidence interval for estimating the mean quantity sold for those days when the price was $6. (6%) 4. Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 where 0 =female and 1=male). The following is a partial result of a computer program that was used on a sample of 20 individuals. Coefficient Standard Error X1 0.6251 0.094 X2 0.9210 0.190 X3 -0.510 0.920 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 84 Error 112 a. Compute the coefficient of determination. (10%) b. Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., X2) is significantly different from zero. Let . (10%) c. At , perform an F test and determine whether or not the regression model is significant. (5%) d. As you note the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient. (5%)