Various doses of a poisonous substance were given to groups of 25 mice and thefollowing results were observed:Dose (mg)X46810121416Number of deathsy1368141620(a) Find the equation of the least squares line fit to these data(b) Estimate the number of deaths in a group of 25 mice who receive a 7 mg dose ofthis poison.

Answered: Image /qna-images/answer/dbf1a713-7d82-4dd1-abd3-6bdc7637fd86.jpg

Answered: Various doses of a poisonous substance…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Suppose a car's city miles per gallon rating can be determined by the car's weight. The means and standard deviations of these variables and the correlation coefficient between them are reported in the following table. Determine the coefficients of the least squares line for predicting a car's miles per gallon rating from its weight. Report the equation of this line. 2 decimals for "a" and 5 decimals for "b"
Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: Ey = 1,134 x= 3.642, =93,110, = 948622, and Txy = 295.54 Find the least squares prediction equation for predicting the number of games won, y, using a straight-line relationship with the team's batting average, x.
In 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 calculations
In a study of 2000 model cars, a researcher computed the least-squares regression line of price (in collars) on horsepower. He obtained the following equation of this regression line: Price = -7000 + 170 horsepower Based on the least-squares regression line, what would we predict the cost of a 2000 model car with horsepower equal to 230 to be (assuming no extrapolation error). Please show calculations as tutorial on how to answer the question.
Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is Bags = -151.05 +2.65Temp. On one of the observed days, the temperature was 82 °F and 68 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, Bags, when the temperature is (82\ \text (°F. J\\) Enter your answer as a whole number, rounding if necessary. Bags = 1.11 residual Incorrect Using the predicted value you just found, compute the residual at this temperature. 1.11 Incorrect ice bags ice bags
In a study of 2005 model cars, a researcher computed the least squares regression line of miles per gallon (mpg) on weight (in pounds). They obtained the following equation for this line: mpg = 34.576 - 0.007weight Based on the least-squares line, we would predict a 2005 model car with weight equal to 3,000 pounds would have a mpg of Fill in the blank with: ##.###
A student studying statistics examined whether a relationship exists between the city miles per gallon (mpg) and highway miles per gallon (mpg) for cars and trucks. The miles per gallon of a vehicle describe the typical number of miles the vehicle can drive on one gallon of gas. Using a random sampleof 50 cars and trucks, the student obtained the least squares regression equation: predicted highway mpg = 1.14 .(city mpg) + 5.8 a. Predict the highway mpg for a vehicle that gets an average of 24 miles per gallon when driving in the city. b. Describe the meaning of the number 1.14 in the regression equation above?
7) An accountant wishes to predict direct labor cost (y) on the basis of the batch size (x) of a product produced in a job shop. Using data for 12 production runs, the least squares line has an intercept of 18.488 and a slope of 10.146. Please interpret the meanings of the intercept and the slope in this context. Do you think that the interpretation of the intercept does make practical sense?
A world wide fast food chain decided to carry out an experiment to assess the influence of income on number of visits to their restaurants or vice versa. A sample of households was asked about the number of times they visit a fast food restaurant (X) during last month as well as their monthly income (Y). The data presented in the following table are the sums and sum of squares. (use 2 digits after decimal point) ∑ Y = 393 ∑ Y2 = 21027 ∑ ( Y-Ybar )2 = SSY = 1720.88 ∑ X = 324 ∑ X2 = 14272 ∑ ( X-Xbar )2 = SSX = 1150 nx=8 ny=11 ∑ [ ( X-Xbar )( Y-Ybar) ] =SSXY=1090.5 PART A Sample mean income is Answer Sample standard deviation of income is Answer 90% confidence interval for the population mean income (hint: assume that income distributed normally with mean μ and variance σ2) is [Answer±Answer*Answer] 90% confidence interval for the population variance of income (hint: assume that income distributed normally with mean μ and variance σ2) is…
A researcher wishes To determine the relationship between the number of Cows(in thousands) in counties in southwestern Pennsylvania and the milk production ( in millions of pounds.) After computing the least squares regression line, it is determined that r^2=0.9972. Which of the following is the correct interpretation of this value? Answer Choices: A.) none of the other answers is a correct interpretation B.) About 99.72% of the changes in the number of cows are explained by changes in milk production C.) About 99.72% of the change in milk production are explained by changes in the number of cows.
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
Apply the linear least-squares method to each set of data to obtain a mathematical model showing the relationships between variables.

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