Concept explainers
Thickness of dust on solar cells. The performance of a solar cell can deteriorate when atmospheric dust accumulates on the solar panel surface. In the International Journal of Energy and Environmental Engineering (December 2012). researchers at the Renewable Energy Research Laboratory. University of Lucknow (India), estimated the relationship between the dust thickness and the efficiency of a solar cell. The thickness of dust (in millimeters) collected on a solar cell was measured three times per month over a year-long period. Each time the dust thickness was measured, the researchers also determined the percentage difference (before minus after dust collection) in efficiency of the solar panel. Data (monthly averages) for the 10 months in which there was no rain are listed in the accompanying table.
a. Fit the linear model, y = β0 + β1x + ε, to the data where y = efficiency and x = average dust thickness.
b. Evaluate the model, statistically. Do you recommend using the model in practice?
Month | Efficiency (% change) | Average Dust Thickness (mm) |
January | 1.5666 | 0.00024 |
February | 1.9574 | 0.00105 |
March | 1.3707 | 0.00075 |
Apr« | 1.9563 | 0.00070 |
May | 1.6332 | 0.00142 |
June | 1.8172 | 0.00055 |
July | 0.9202 | 0.00039 |
October | 1.8790 | 0.00095 |
November | 1.5544 | 0.00064 |
December | 2.0198 | 0.00065 |
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Statistics for Business and Economics (13th Edition)
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardFind the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forwardIf your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?arrow_forward
- Can the average rate of change of a function be constant?arrow_forwardTable 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forward
- Please show the complete solution and write readable thanks.arrow_forwardSheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if her glucose level is above 155 milligrams per deciliter (mg/dl) one hour after a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 140 mg/dl and σ = 11 mg/dl.Let X = Sheila's measured glucose level one hour after a sugary drink(a) P(X > 155) = (Use 3 decimal places)Suppose measurements are made on 3 separate days and the mean result is compared with the criterion 155 mg/dl.(b) P(X > 155) = (Use 3 decimal places)(c) What sample mean blood glucose level is higher than 95% of all other sample mean blood glucose levels? Hint: this requires a backward Normal calculation. (Use 2 decimal places)arrow_forwardDescribe three approaches to modeling seasonality in a regression forecast.arrow_forward
- Seedlings of understory trees in mature tropical rainforests must survive and grow using intermittent flecks of sunlight. How does the length of exposure to these flecks of sunlight (fleck duration) affect growth? Researchers experimentally irradiated seedlings of the Southeast Asian rainforest tree with flecks of light of varying duration while maintaining the same total irradiance to all the seedlings. Below is the data. Fit a linear model to the data. Tree Mean Fleck (min) Relative growth rate (mm/mm/week 1 3.4 0.013 2 3.2 0.008 3 3 0.007 4 2.7 0.005 5 2.8 0.003 6 3.2 0.003 7 2.2 0.005 8 2.2 0.003 9 2.4 0 10 4.4 0.009 11 5.1 0.01 12 6.3 0.009 13 7.3 0.009 14 6 0.016 15 5.9 0.025 16 7.1 0.021 17 8.8 0.024 18 7.4 0.019 19 7.5 0.016 20 7.5 0.014 21 7.9 0.014 a)What is the rate of change in relative growth…arrow_forwardResearchers collected samples of water from streams in a mountain range to investigate the effects of acid rain. They measured the pH (acidity) of the water and classified the streams with respect to the kind of substrate (type of rock over which they flow). A lower pH means the water is more acidic. The plot to the right shows the pH of the streams by substrate (limestone, mixed, or shale). Selected parts of a software analysis comparing pH of streams with mixed and shale substrates are shown below. Complete parts a through c. 2-Sample t-test of μ1−μ2=0, Difference Between Means=0.195 t-Statistic=5.30 w/125 df, P≤0.0001 a) State the null and alternative hypotheses for this test. Choose the correct answer below. A. H0: μM−μS=0; HA: μM−μS≠0 B. H0: μM−μS≤0; HA: μM−μS>0 C. H0: μM−μS≥0; HA: μM−μS<0 D. H0: μM−μS≠0; HA: μM−μS=0 Part 2 b) From the information you have, do the assumptions and conditions appear to be met? Which…arrow_forwardUse a smoothing constant ALPHA = 0.8 and calculate the forecasted value and smoothing valuearrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning