Exam 13: Simple Linear Regression

The Regression Sum of Squares (SSR) can never be greater than the Total Sum of Squares (SST).

TABLE 13-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 13-4, the least squares estimate of the Y-intercept is ________.

TABLE 13-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 13-4, suppose the managers of the brokerage firm want to construct a 99% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients. The t critical value they would use is ________.

TABLE 13-13 In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score which is the sum of the math, science and reading scores as the dependent variable on 35 states that participated in a study. The table includes only partial results. -Referring to Table 13-13, what percentage of the variation in composite score can be explained by the variation in spending per student?

TABLE 13-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following Excel output. Note: 2.94942E-07 = 2.94942*10⁻⁷ -Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the appropriate null and alternative hypotheses are, respectively,

TABLE 13-8 It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. -Referring to Table 13-8, the interpretation of the coefficient of determination in this regression is

The width of the prediction interval for the predicted value of Y is dependent on

TABLE 13-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: -Referring to Table 13-2, what percentage of the total variation in candy bar sales is explained by prices?

Referring to Table 13-2, what is for these data?

TABLE 13-13 In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score which is the sum of the math, science and reading scores as the dependent variable on 35 states that participated in a study. The table includes only partial results. -Referring to Table 13-13, the conclusion on the test of whether spending per student affects composite score using a 5% level of significance is

TABLE 13-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 13-4, ________ % of the total variation in sales generated can be explained by the number of new clients brought in.

TABLE 13-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 13-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. At a level of significance of 0.01, the decision that should be made implies that the number of new clients brought in ________ (had or did not have) a positive impact on the amount of sales generated.

TABLE 13-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 13-4, the standard error of the estimated slope coefficient is ________.

TABLE 13-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application. Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded. Below is the regression output: Note: 4.3946E-15 is 4.3946 × -Referring to Table 13-12, the value of the measured t test statistic to test whether the amount of time depends linearly on the number of loan applications recorded is

TABLE 13-6 The following Excel tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course. -Referring to Table 13-6, which of the following statements is true?

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.744 when testing H₀: ρ = 0 against the one-sided alternative H₁: ρ < 0. To test H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0 at a significance level of 0.1, the p-value is

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: -Referring to Table 13-10, what is the value of the standard error of the estimate?

TABLE 13-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below. -Referring to Table 13-3, the total sum of squares (SST) is ________.

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, the null hypothesis that there is no linear relationship between revenue and the number of downloads should be rejected at a 5% level of significance.

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what is the value of the test statistic for testing whether there is a linear relationship between revenue and the number of downloads?