The data from a random sample of 75 students was used to fit a least squares regression line relating test scores to the number of hours spent playing Left for Dead 2 each week. The explanatory variable (hours spent playing Left for Dead 2) had a range of 0- 18 and the response variable (test score) ranged from 55 - 99%. The resulting prediction equation is y = 99 - 4.3x. Furthermore, the correlation coefficient is 0.85. Determine if the following statements are TRUE or FALSE. a. The association between hours playing Left for Dead 2 and test score is strong. b. As hours spent playing Left for Dead 2 decreases, test score decreases.

The data from a random sample of 75 students was used to fit a least squares regression line relating test scores to the number of hours spent playing Left for Dead 2 each week. The explanatory variable (hours spent playing Left for Dead 2) had a range of 0- 18 and the response variable (test score) ranged from 55 - 99%. The resulting prediction equation is y = 99 - 4.3x. Furthermore, the correlation coefficient is 0.85. Determine if the following statements are TRUE or FALSE. a. The association between hours playing Left for Dead 2 and test score is strong. b. As hours spent playing Left for Dead 2 decreases, test score decreases.

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

An article included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 17 percent of the variance in first-year college grades. GPA was second at 15.2 percent, and SAT I was last at 13.1 percent." If the data from this study were used to fit a least squares line with y = first-year college GPA and x = high school GPA, what would the value of r2 have been? R2 ____________________%
Given the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?
When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?
The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.
A multiple regression includes two regressors: Yi = b0 + b1X1i +b2X2i + ui. What is the expected change in Y if X1 increases by 8 unitsand X2 is unchanged? What is the expected change in Y if X2 decreasesby 3 units and X1 is unchanged? What is the expected change in Y if X1increases by 4 units and X2 decreases by 7 units?
A simple random sample of 100 men aged 25–34 averaged 70 inches in height, and had astandard deviation of 3 inches. Their incomes averaged $34,900 and had a standarddeviation of $17,200. Fill in the blank: From the least-squares line, we would predict thatthe income of a man 70 inches tall would be _____.a) less than $34,900.b) greater than $34,900.c) equal to $34,900.d) We cannot tell unless we know the correlation.
Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.904 and the least squares regression line is y=0.208x+11.736. Complete parts (a) and (b) below.
What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places.
on the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?
If all the points in a scatter diagram lie on the least squares regression line, what must be the coefficient of correlation equal to
In a random sample of pediatric patients at a local hospital, the age of a patient and the patient's height have a correlation of 0.8. If we use the age of the patients to predict their height, which of the following is a correct statement? a Sixty-four percent of the time, the least squares regression line accurately predicts height. b About 80% of a person's height can be explained by age, according to the regression line relating height and age. c Sixty-four percent of the variation in height can be explained by the variation in the age of a patient. d The least squares regression line relating height to age will have a slope of approximately 0.8. e About 80% of the time, age will correctly predict the height.
If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data _____. Select one: A. is 0 B. could be any value between -1 and 1 C. is either 1 or -1, depending upon whether the relationship is positive or negative D. is 1