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- Match the coefficient of determination to the scatter diagram. The scales on the x-axis and y-axis are the same for each scatter diagram (a) R2 0.90, (b) R2 0.58, (c) R2 =1 (a) Scatter diagram Explanatory (b) Scatter diagram (c) Scatter diagram Explanatory III ExplanatoryA business analyst found a linear relationship between the predicted profit (in thousands of dollars) with the amount of employees hired (think of the units as per person). The resulting regression equation and coefficient of determination were found to be: ŷ = 10 + 4.5x R² = 72% a) Interpret the slope and y-intercept using the guidelines learned in class. b) Find the predicted profit when the you hire 5 employees. c) Suppose that the true profit when 5 employees are hired is $42 thousand dollars. Find the residual. d) What is the correlation coefficient? Round to three decimal places. e) What is the strength of the correlation coefficient?use the following information: A study of the mail survey response rate patterns of people aged 60- 90 found a prediction equation of ŷ = 90.2-0.6x relating x = age (in years) and y = percentage of people who responded to the survey. 6) Interpret the slope in the linear equation (ŷ = 90.2-0.6x). Using the linear prediction equation, find the predicted response rate for a (i) 60-year-old and (ii) 90-year-old. Predicted response rate for 60-year-old: Predicted response rate for 90-year-old:
- please explain with an example.The table shows data collected on the relationship between the average daily temperature and time spent watching television. The line of best fit for the data is yˆ=−0.66x+88.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Temperature (Degrees) Minutes Watching Television 35 66 45 58 55 52 65 46 (a) According to the line of best fit, what would be the predicted number of minutes spent watching television for an average daily temperature of 46 degrees? Round your answer to two decimal places, as needed. Provide your answer below: The predicted number of minutes spent watching television is .A fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the residence and the nearest fire station. The study was conducted in a large suburb of a major city; a sample of fifteen recent fires in the suburb was selected. The amount of damage, y (£000), and the distance, r (km), between the fire and the nearest fire station are given in the following table. 3.4 1.8 4.6 2.3 3.1 5.5 0.7 3.0 y 26.2 17.8 31.3 23.1 27.5 36.0 2.1 y 19.6 31.3 24.0 17.3 43.2 36.4 26.1 14.1 22.3 2.6 4.3 1.1 6.1 4.8 3.8 (a) Fit a simple linear regression model to these data. Check if the residual plots give any reason to doubt the usual assumptions of the model. (b) Write a short report giving your conclusions. You do not need to upload the output from R. Include a possible interpretation of the intercept and slope parameters.
- A random sample of 136 adults were asked to report the number of hours per week the spent on a computer and their number of years of education. The linear model equation below describes the relationship between the mean computers hours and years of education. computers == 9.12 ++ 0.8 ×× education Based on this linear model, which of the following statements is correct? a) An adult who has no years of education is expected to spend 9.12 hours per week on a computer. b) An adult who has 1 more year of education than another is expected to spend 9.12 more hours per week on a computer. c) An adult who spends 1 more hour per week on a computer than another is expected to have had 9.12 more years of education. d) An adult who spend zero hours per week on a computer is expected to have 9.12 years of education.A biologist was recording various temperatures (in degrees Celsius) and predicting the amount of glucose produced by a plant (in milligrams). Suppose the linear equation was the following: ?̂ = 12.7 − 0.223? d) Suppose the correlation coefficient was −0.12. How would you classify the correlation between temperature and amount of glucose?If the regression line showing the effect of education on income has a slope of 1000. a) the variables are not related b) the Y intercept would be 1.00 c) every change in education increases income d) every year of education increases income by 1000
- The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant ŷ = 2.35+2.20X. Suppose, for a selected workstation, the labor input is 5, the predicted output is?Several surveys in the United States and Europe have asked people to rate their happiness on a scale of 3 = "very happy," 2 = "fairly happy," and 1 = "not too happy," and then tried to correlate the answer with the person's income. For those in one income group (making $25,000 to $55,000) it was found that their "happiness" was approximately given by y = 0.065x - 0.613, where x is in thousands of dollars. Find the reported "happiness" of a person with the following incomes (rounding your answers to one decimal place). (a) $30,000 (b) $50,000 (c) $55,000A trendline is given to depict enrollment at a local college where x is the year and y represents enrollment. Y=178.09x-353194 Use the rrendline ro estimate the enrollment for 2009. Round to the nearest whole number.