Math Problem Statement

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) through​ (d) below. LOADING... Click here to view the weight and gas mileage data. Question content area bottom Part 1 ​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ModifyingAbove y with caretequals    enter your response herexplus​(    enter your response here​) ​(Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as​ needed.) Part 2 ​(b) Interpret the slope and​ y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. ​(Use the answer from part a to find this​ answer.) A. For every pound added to the weight of the​ car, gas mileage in the city will decrease by    enter your response here ​mile(s) per​ gallon, on average. It is not appropriate to interpret the​ y-intercept. B. For every pound added to the weight of the​ car, gas mileage in the city will decrease by    enter your response here ​mile(s) per​ gallon, on average. A weightless car will get    enter your response here miles per​ gallon, on average. C. A weightless car will get    enter your response here miles per​ gallon, on average. It is not appropriate to interpret the slope. D. It is not appropriate to interpret the slope or the​ y-intercept. Part 3 ​(c) A certain​ gas-powered car weighs 3629 pounds and gets 19 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight? The estimated average miles per gallon for cars of this weight is    enter your response here miles per gallon. The miles per gallon of this car is ▼ above below average for cars of this weight. ​(Round to three decimal places as​ needed.) Part 4 ​(d) Would it be reasonable to use the​ least-squares regression line to predict the miles per gallon of a hybrid gas and electric​ car? Why or why​ not? A. ​No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of nequals10. B. ​Yes, because a hybrid gas and electric car is partially powered by gas. C. ​Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of nequals10. D. ​No, because a hybrid gas and electric car is a different type of car.

Solution

To help you with these parts, I’ll need the data for the weight and gas mileage of various domestic cars. Could you upload that data, or if possible, provide it directly here?

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Data Analysis

Formulas

y = mx + b (Least-Squares Regression Line)

Theorems

Interpretation of the slope and intercept in a regression line

Suitable Grade Level

Grades 10-12