A sports analyst determines that the number of points Scored in a basketball game is related to the number of shots taken during the game. The least-squares regression line is ŷ = 5.0 + 1.2x, where ŷ is the predicted number of points scored and x is the number In one game, a team takes 50 shots and the residual is -10. How many points were scored by this team in this game? O 45 of shots taken. O 55 O 65 O 75

A sports analyst determines that the number of points Scored in a basketball game is related to the number of shots taken during the game. The least-squares regression line is ŷ = 5.0 + 1.2x, where ŷ is the predicted number of points scored and x is the number In one game, a team takes 50 shots and the residual is -10. How many points were scored by this team in this game? O 45 of shots taken. O 55 O 65 O 75

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

See similar textbooks

Similar questions

A recent campus bookstore survey sought to determine if there is a relationship between new textbook prices y (dollars) and the number of pages in the book x. The resulting least-squares regression line for the study is y = 38.04 + 0.12x. What is the predicted price when the number of pages is 75?
A recent campus bookstore survey sought to determine if there is a relationship between new textbook prices y (dollars) and the number of pages in the book x. The resulting least-squares regression line for the study is y = 38.04 + 0.12x. What is the predicted price when the number of pages is 75? Enter your answer as a dollar.
An engineer wants to determine how the weight of a gas-powered car, x, affects the gas mileage, y. 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 and why not?
A regression analysis between weight (y in pounds) and height (x in inches) resulted in following least squares line: y^= 120+5x. this implies that if the height is increased by 1 inch, the weight is expected ?
The following data is about the number of turns required to break a certain type of forged alloy bar, as well as the percentages of two alloying elements present in the metal. A) Fit a least squares regression plane and use its equation to estimate the number of turns required to break one of the bars, when x1 = 2.5 and x2 = 12 In the tabley = number of turnsx1 =% of element Ax2 =% of element B
In general, what is true about the relationship between the Sum of Squared Residuals in the restricted and unrestricted model? a. SSRr < SSRur b. SSRr > SSRur c. SSRr = SSRur d. SSRr = R-squared * SSRur
The data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squares
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.
One day in gym class students took a physical fitness test bydoing push-ups and sit-ups. The standard deviation of the number of sit-ups they were able to do was 7 and the stand-ard deviation of the number of push-ups was 2. A Statistics student used these data to create a least squares regressionline to predict the number of sit-ups a student was able to dobased on the number of push-ups the student did. Which ofthe following could NOT be the slope of that line?A) -2 B) -0.5 C) 1D) 3 E) 4
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas use y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65F) over a 23-month period. He then computed the least squares regression line for predicting y from x and found it to be, ŷ=85+16x How much, on average, does gas used increase for each additional degree-day? The predicted amount of gas used when the outside temperature is 20 degree- days.
Suppose a least-squares regression line is given by y=4.302x−3.293. What is the mean value of the response variable if x=20? μy20=_______? (Round to one decimal place as needed.)
A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?