Back[DATA] The following data represent the height (inches) of boys between the ages of 2 and 10 years.
d. Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.
[DATA] Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket.
a. What is the most likely explanatory variable in these data? Explain your reasoning.
[DATA] Concrete As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete:
a. Treating the 7-day strength as the explanatory variable, x, determine the estimates of β₀ and β₁.
[DATA] Concrete As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete:
c. Determine sb_1.
[DATA] Graduation Rates PayScale reports statistics on colleges and universities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_24 using the file format of your choice for the version of the text you are using. The data contain the four-year cost and graduation rate for over 1300 colleges and universities. Do schools that charge more have higher graduation rates? The variable “4 Year Cost” represents the four-year cost of attending the college or university. The variable “Grad Rate” represents the percentage of incoming freshman who graduate within six years.
f. What proportion of the variability in graduation rates is explained by the cost of attending?
Suppose a least-squares regression line is given by ŷ = 4.302x – 3.293. What is the mean value of the response variable if x = 20?
[DATA] Invest in Education Go to www.pearsonhighered.com/sullivanstats to obtain the data file 12_3_17. The variable “Cost” represents the four-year cost including tuition, supplies, room and board, the variable “Annual ROI” represents the return on investment for graduates of the school—essentially how much you would earn on the investment of attending the school. The variable “Grad Rate” represents the graduation rate of the school.
c. What is the mean annual ROI for a four-year school whose cost is \$180,000?
[DATA] CEO Performance (Refer to Problem 33 in Section 4.1) The following data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and the company’s stock performance in 2017.
b. Assuming the residuals are normally distributed, test whether a linear relation exists between compensation and stock return at the alpha = 0.05 level of significance
[DATA] CEO Performance (Refer to Problem 33 in Section 4.1) The following data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and the company’s stock performance in 2017.
d. Based on your results to parts (b) and (c), would you recommend using the least-squares regression line to predict the stock return of a company based on the CEO’s compensation? Why?
[DATA] Bear Markets (Refer to Problem 34, Section 4.1) A bear market is a market condition in which the price of the security falls. A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P500 (a group of 500 stocks).
b. Assuming the residuals are normally distributed, test whether a linear relation exists between the number of months of a bear market and percent change at the alpha = 0.05 level of significance.
[DATA] Bear Markets (Refer to Problem 34, Section 4.1) A bear market is a market condition in which the price of the security falls. A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P500 (a group of 500 stocks).
d. Based on your results to parts (b) and (c), would you recommend using the least-squares regression line to predict the percent change in the S&P500 during a bear market? Why?
"[DATA] Credit Scores [See Problem 12 in Section 12.3] An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The data represent the interest rate (in percent) a bank might offer on a 36-month auto loan for various FICO scores.
b. Determine the slope of the least-squares regression line between credit score and interest rate."
"[DATA] An Unhealthy Commute [See Problem 11 in Section 12.3] The following data represent commute times (in minutes) and a score on a well-being survey.
b. Determine the slope of the least-squares regression line between commute time and well-being score."
What do the y-coordinates on the least-squares regression line represent?
In the least-squares regression model, yi = β1xi + β0 + εi, εi is a random error term with mean ______ and standard deviation σεi = ______.