Concept explainers
Video Games and Grade-Point Average Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week. , to the cumulative grade-point average. , of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.
(a) Explain why the number of hours spent playing video games is the independent variable and cumulative grade-point average is the dependent variable.
(b) Use a graphing utility to draw a
(c) Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation.
(d) Interpret the slope.
(e) Predict the grade-point average of a student who plays video games for 8 hours each week.
(f) How many hours of video game playing do you think a student plays whose grade-point average is ?
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
- One of the biggest changes in higher education in recent years has been the growth of online universities. The Online Education Database is an independent organization whose mission is to build a comprehensive list of the top accredited online colleges. The following table shows the retention rate (%) and the graduation rate (%) for 29 online colleges.a). Use Excel Data Analysis Tool – Regression to get the relationship between the two variables;b). Create a scatter diagram for the two variables and display regression equation and R square on chart, then explain the relationship between the variables;c). Did the estimated regression equation provide a good fit?d). Suppose you were the president of South University. After reviewing the results, would you be able to use the regression result for forecasting. College RR(%) GR(%) Western International University 7 25 South University 51 25 University of Phoenix 4 28 American InterContinental University 29 32 Franklin…arrow_forwardQ1: Please use the data set to create a regression equation or a regression line that can reflect the relationship between wealth and level of education in CA counties. NOTES: You are required to: 1) clearly state what is the dependent variable (Y) and what is the independent variable (X); 2) correctly calculate the associated slope and intercept. Q2: Please predict the related median household income when there is 70% of population over 25 with BA degree and higher. Median Household Income ($) % of population over 25 with BA degree and higher 100,929 42.1 71,348 20.5 59,961 25.0 69,588 21.1 108,689 39.4 90,996 32.1 63,284 19.5 53,746 27.5 58,528 13.4 66,834 15.2…arrow_forwardA river was found to be contaminated with toxins at a concentration of 0.006 grams per cubic meter near a mine tailings pond. 1500 meters away, the concentration was found to be 0.004 grams grams per cubic meter. Assume the concentration drops off linearly going downstream, and it is uniform over the 50 square meter cross section. How many grams of toxins do you estimate have leaked from the tailings pond? a. 675 grams b. 650 grams c. 700 grams d. 625 gramsarrow_forward
- Spring is a peak time for selling houses. The file SpringHouses contains the selling price, number of bathrooms, square footage, and number of bedrooms of 26 homes sold in Ft. Thomas, Kentucky, in spring 2018 (realtor.com website) Click on the datafile logo to reference the data. DATA file a. The Excel output for the estimated regression equation that can be used to predict the selling price given the number of bathrooms, square footage, and number of bedrooms in the house: SUMMARY OUTPUT Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression statistics Regression Residual Total Multiple R R Square ANOVA Adjusted R Square Standard Error Observations 0.7429 0.5519 0.4907 61948.6931 Regression statistics Regression Residual Total df Intercept Sq Ft Beds Lower 95% 0.9353 -145129.5298 Intercept Baths 0.9528 -49383.5243 0.0180 Sq Ft Beds 0.0326 Does the estimated regression equation provide a good fit to the data? Explain. Hint: If R is greater than 45%, the…arrow_forwardThe data set Pain contains hypothetical data for a clinical trial of a drug therapy to control pain. The clinical trial investigates whether adverse responses increase with larger drug doses. Subjects receive either a placebo or one of four drug doses (1, 2, 3, or 4 units). An adverse response is recorded as Adverse = 'Yes'; otherwise, it is recorded as Adverse = 'No'. The number of subjects for each drug dose and response combination is contained in the variable Count. (a) Construct a contingency table that corresponds to the data set created above. What type of variable is Dose? (B) Compute the sample proportions of adverse responses at each dose level. Do you observe any trend in the proportion of adverse responses with respect to dose level? (C) Conduct a Cochran-Armitage trend test at the 5% significance level to address the interests of the trial.arrow_forwardIn order for a linear model between variable and age to be appropriate, the plot must have no pattern right?arrow_forward
- Pa.n.narrow_forwardThe electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x₁), the number of days in the month (x₂), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in the following table: Y 240 236 270 274 301 316 270 296 267 276 288 261 25 31 45 60 65 72 80 84 75 60 50 38 X2 24 21 24 25 25 26 25 25 24 25 25 23 Fit a multiple linear regression to predict power (y) using x1, X2 X3, and X4. Calculate R2 for this model. Round your answer to 3 decimal places. 91 90 88 87 91 94 87 86 88 91 90 89 X4 100 95 110 88 94 99 97 96 110 105 100 98arrow_forwardIn a regression model, if every data point is exactly along the regression line, thenA. the coefficient of correlation would be 0B. the coefficient of correlation would be -1 or 1C. the coefficient of determination would be 0D. the coefficient of determination would be -1arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning