Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Chapter 7.4, Problem 1JC
A
1. You go to an open house and find that the house is 1 SD above the
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Researchers record the fuel consumption of a car y (in miles per gallon) at various speeds x (in miles per hour). Using software, they determine that the least-squares regression line of their data is
y^=70.243−0.329x
If the observed fuel consumption of the car was y = 49y=49 mpg while moving at a speed of x = 20x=20mph, what would be the error (i.e., residual) in the predicted fuel consumption at this speed found with the least-squares regression line?
(Do not round your answer.)
A newspaper advertisement in the Straits Times of Singapore contained pictures of diamond rings and listed their prices, diamond weight (in carats), and gold purity. Based on data for only the 20-carat gold ladies’ rings in the advertisement, the least-squares regression line for predicting price (in Singapore dollars) from the weight of the diamond (in carats) is:
price = 259.63 + 3721.02 carats
What does the slope of this line say about the relationship between price and number of carats?
A group of 13 healthy children and adolescents participated in a phycological study designed to analyze the relationship between age and average total sleep time (ATST). To obtain a measure for ATST (in minutes), recordings were taken on each subject on three consecutive nights and then averaged. Results are provided to you in Sleep&Age.xlsx Download Sleep&Age.xlsx file. (2 points) Determine the least-squares regression line for predicting average total sleep time using age. (2 points) Make a scatter plot of the data with ATST on the y-axis (vertical axis) and Age on the x-axis (horizontal axis) with least squares regression line overlaid on the top (i.e.: obtain the fitted line plot). Make sure to attach the plot below. (7 points) Check the assumptions for the simple linear regression. Attach any plots you used check the assumptions and comment on them. (7 points) We want to see if the average sleep time decreases as the children grow older. Write the appropriate null and…
Chapter 7 Solutions
Intro Stats
Ch. 7.4 - A scatterplot of house Price (in dollars) vs....Ch. 7.4 - A scatterplot of house Price (in dollars) vs....Ch. 7.4 - A scatterplot of house Price (in dollars) vs....Ch. 7.4 - A scatterplot of house Price (in dollars) vs....Ch. 7.4 - A scatterplot of house Price (in dollars) vs....Ch. 7.4 - Prob. 6JCCh. 7.6 - Prob. 7JCCh. 7.6 - Prob. 8JCCh. 7.6 - Prob. 9JCCh. 7 - True or false If false, explain briefly. a) We...
Ch. 7 - True or false II If false, explain briefly. a)...Ch. 7 - Prob. 3ECh. 7 - Prob. 4ECh. 7 - Bookstore sales revisited Recall the data we saw...Ch. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - Prob. 8ECh. 7 - Bookstore sales once more Here are the residuals...Ch. 7 - Prob. 10ECh. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - 14. Disk drives last time Here is a scatterplot of...Ch. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - More cereal Exercise 15 describes a regression...Ch. 7 - Prob. 18ECh. 7 - Another bowl In Exercise 15, the regression model...Ch. 7 - Prob. 20ECh. 7 - Cereal again The correlation between a cereals...Ch. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Residuals Tell what each of the residual plots...Ch. 7 - Real estate A random sample of records of home...Ch. 7 - 30. Roller coaster The Mitch Hawker poll ranked...Ch. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Real estate again The regression of Price on Size...Ch. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - More misinterpretations A Sociology student...Ch. 7 - Real estate redux The regression of Price on Size...Ch. 7 - 38. Another ride The regression of Duration of a...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - 46. Second inning 2010 Consider again the...Ch. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Online clothes An online clothing retailer keeps...Ch. 7 - Online clothes II For the online clothing retailer...Ch. 7 - Prob. 53ECh. 7 - Success in college Colleges use SAT scores in the...Ch. 7 - SAT, take 2 Suppose we wanted to use SAT math...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Drug abuse revisited Chapter 6, Exercise 42...Ch. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - 64. Chicken Chicken sandwiches are often...Ch. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - 70. Birthrates 2009 The table shows the number of...Ch. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Hard water In an investigation of environmental...Ch. 7 - 76. Gators Wildlife researchers monitor many...Ch. 7 - Prob. 77ECh. 7 - Least squares Consider the four points (200,1950),...
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- In Austria ,The amount of money spent on the restoration of a sanctuary and the distinct kangaroo populations present appeared to have negative correlations For investigation of this onserved assocaition ,what can a resecher do to begin his research 1Conduct an experiment 2Calculate the squares of coreealtion coefficient 3Calculate the least squares regression line 4 calculate the corelation coefficient Explain answer in 1 or 2 linesarrow_forwardBattery life has a strong, negative, linear relationship with temperature. If the least-squares regredsion line using x = temperature explains 90% of the variation in battery life, what is the correlation, r, between battery life and temperature.arrow_forwardIn a study of cars that may be considered classics (all built in the 1970s), the least-squares regression line of mileage (in miles per gallon) on vehicle weight (in thousands of pounds) is calculated to be mileage = 45 – 7.5 weightThe mileage for a small Chevy is predicted to be 22 miles per gallon. What was the weight (lbs) of this car? Please show work of calculationsarrow_forward
- A population of marine gastropods has shell lengths that are normally distributed with a mean of 7 mm and a variance of 2.25 mm^2. What proportion of the population will have a shell between 5.5 mm and 8.5 mm?arrow_forwardThe line of best fit is the line that minimizes the total of all the squared residuals true or false?arrow_forwardWhat is the least-squares line approximation to a set of datapoints? How is the line determined?arrow_forward
- A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent. Predict the number of days absent for an employee that lives 5 miles from the hospital.arrow_forwardThe following data table shows the historical data for the first semester 2020, of the amount of sales of the company "IRC", which sells sneakers. Utilizing multiple lineal regression (as shown on the image), find an equation that estimates the number of sneakers sold by the company, based on advertising and revenue. Also, determine the standard error of estimation, the coefficient of determination, and the correlation coefficient. Write down what was the quantity in thousands sold in July if the amount of ads was 8 and the income for each unit was $135arrow_forwardIn a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. Price = – 6677 + 175× Horsepower Based on the least-squares regression line, what would we predict the cost to be of a 1991 model car with horsepower equal to 200? If the actual cost of a 1991 car with 200 horsepower is $27500, what is the residual? Is the predictionan underestimate or an overestimate? What does the slope of 175 and y intercept of (0,-6677) mean in the context of the problem? The coefficient of determination is ?2=84%. Interpret in the context of the problem. Find the correlation and interpret.arrow_forward
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