1. Why are some quantities in nature not exactly measurable?2. Explain how linear regression is used to find the equation that relates two variables.3. In an experiment, you performed linear regression on a set of temperature and time data. Are thetwo variables strongly correlated if the slope of the trend line is:a. almost zero?b. negative?c. positive?4. Data from a certain experiment was plotted on a graph, with their error bars shown:Volume vs temperature908070605040302010-10-51015202530Temperature ("C)a. The measurements of which variable has a larger uncertainty?b. At what temperature does the volume of the system begin to show no overlap with othervolume measurements?Volume (L) II. Using the eyeball method, estimate and draw the best fit line of the data for the following scatter plots:5)6)7)

Introduction - Uncertainty = ∑Xi-μ2n×n-1where , n = size of the population μ= mean

Answered: 1. Why are some quantities in 2.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive? Is the regression coefficient statistically significant? How can you tell?
Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 88 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−0.813+0.177?,h^=−0.813+0.177w, with standard error for the coefficient of ?w equal to 0.448. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
1.
A researcher that there is a linear association between the level of potassium content (y) in milligrams and the amount of fiber (x) in grams in cereal. The regression line for the data is computed to y=37+28x rate. It was also computed that r=.59 A. What does the value . 59 tell you? B. What does the value 37 tell you? C. What does the value 28 tell you ? 2. For the line in question 1 what percentage of variability in potassium can be explained by variability in fiber?
Different patients are randomly selected and measured for pulse rate and body temperature. Using technology with x representing the pulse rates and y representing temperatures, we find that the regression equation has a slope of -0.007 and a y-intercept of 95.6. a. What is the equation of the regression line? b. What does the symbol y represent? a. Choose the correct answer below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) OA. The equation is Inx=+(y. OB. The equation is Iny=( OC. The equation is y=+x OD. The equation is x=+y b. The symbol y represents value of the actual the mean a predicted ▼ C
Develop a scatterplot and explore the correlation between customer age and net sales by each type of customer (regular/promotion). Use the horizontal axis for the customer age to graph. Find the linear regression line that models the data by each type of customer. Round the rate of changes (slopes) to two decimal places and interpret them in terms of the relation between the change in age and the change in net sales. What can you conclude? Hint: Rate of Change = Vertical Change / Horizontal Change = Change in y / Change in x
Ariel was running analyses over and over in census data and came across a correlation between weight and debt (r=.78). Independent variable is weight and dependent variable is debt. b) Curious Ariel noted some statistics on these weight (M=160lb, SD=15lb) and debt (M=196k, SD=20k). If Ariel wanted to calculate a regression equation, what would her slope and intercept be?
Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 85 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−4.273+0.834?,h^=−4.273+0.834w, with standard error for the coefficient of ?w equal to 0.242. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
I. Show complete solutions. Simple Linear Regression and Correlation: a.) Results of a study on the occurrence of sodium and chloride in surface streams in a coastal area. The following data are chloride concentration (y) in mg/liter and road-way area in the watershed (x) in %. Y 0.24 4.6 1. What is the value of the correlation coefficient? 2. What is the interpretation for this case? 3. What is the estimated chloride concentration if road way 0.3 6.4 0.45 9.8 area in the watershed is 1.30% 0.75 10.7 4. What is the equation of the prediction line? 0.57 10.6 0.75 10.9 0.4 11.7 0.8 12.5 0.6 14 0.78 14.7 0.85 15.1 0.68 18.3 0.69 19.2 1.4 23.1 1.15 27.3 1.05 27.7 1.69 32 1.62 38.4
Many small companies buy advertising without considering its effect. The marketing manager is trying to make the case that "you have to spend money to make money." Spending on billboard advertise ments, in the manager's opinion, has a direct effect on sales. These are records for 7 months in 1000s: Monthly expenditure on 21 25 billboards 16 42 34 10 19 Monthly sales Develop a regression estimating equation. If the monthly expenditure on billboards is 20,000/- what is the monthly sale generated 34 14 48 32 26 29 20
Suppose that a simple linear regression model is appropriate for describing the relationship between y = house price (in dollars) and x = house size (in square feet) for houses in a large city. The population regression line is y = 22,500 + 43x and ?e = 4,000. b) Approximately what proportion of 2,000 sq ft homes would be priced over $110,000? (You may need to use a table. Round your answer to four decimal places.) Approximately what proportion of 2,000 sq ft homes would be priced under $100,000? (You may need to use a table. Round your answer to four decimal places.)
Which of the following statements best describes linear regression? A measure of the degree of dependence between two variables. A statistical technique using pairs of data and identifying a line which ‘best fits’ all of the pairs of observations. A measure of the proportion of changes in the dependent variable which can be explained by a change in the independent variable. Shows individual costs against their associated activity levels but makes no attempt to identify a linear relationship between them.

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