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- 1. Prior to being hired, the ve salespersons for a computer store were given a standard sales aptitude test. For each individual, the score achieved on the aptitude test and the number of computer systems sold during the first 3 months of their employment are shown in the attached image. (a) Determine the least-squares regression line and interpret its slope. (b) Estimate, for a new employee who scores 60 on the sales aptitude test, the number of units the new employee will sell in her first 3 months with the company. (c) Find the standard error of estimate. (d) Find the r-square of the model.(g) Compute the sum of the squared residuals for the least-squares regression line found in part (d).5/15 compute the sum of the squared residuals for the least squares regression line found in part a. Type an integer or a decimal.
- The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for 5 randomly selected states in the United States. Compute the least-squares regression line for predicting math proficiency from reading proficiency. State Percent Proficientin Reading Percent Proficientin Mathematics Illinois 75 70 North Carolina 71 73 California 60 59 Georgia 67 64 Florida 66 68 Send data to Excel The equation for the least squares regression line is y = . Round the slope and y -intercept to four decimal places as needed.An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.11/15 find the least squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. Round to three decimal places as needed.
- 2. An article in the Tappi Journal (March, 1986) presented data on green liquor Na2S concentration (in grams per liter) and paper machine production (in tons per day). The data (read from a graph) are shown as follows: (a) Fit a simple linear regression model with y green liquor Na2S concentration and x production. Draw a scatter diagram of the data and the resulting least squares fitted model.(b) Find the fitted value of y corresponding to x = 910 and the associated residual.The regional transit authority for a major metropolitan area wants to determine whetherthere is any relationship between the age of a bus and the annual maintenance cost. Asample of 10 buses resulted in the following data. Age of Bus (year) Maintenance Cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 a. Develop the least squares estimated regression equation.b. Test to see whether the two variables are significantly related with α = .5.c. Did the least squares line provide a good fit to the observed data? Explain.d. Develop a 95% prediction interval for the maintenance cost for a specific bus thatis 4 years old.2. A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Php millions) for each of 22 movies in the year that they were released and the DVD revenue (in Php millions) in the following year are shown below and stored in (pic) a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.
- A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be ŷ =−0.2390+0.044x. This line, along with a scatter plot of her data, is shown below.The data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squaresAn administrator wants to investigate the relationship between the numbers of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected. Distance to Work (miles) 2 4 6 6 9 8 10 12 12 15 Number of Days Absent 8 5 8 6 6 4 6 3 5 3 Develop the least square regression line to predict the number of days absent based on the distance to work. Enter the regression coefficients in xx.xxx format. Round the value to three decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the coefficient is negative. Do not include plus sign in your response. For example, if the coefficient is +6.1563 then enter 06.156 as your answer, if the coefficient is -0.54765 then enter -00.548 and if the answer is -1.6435 then enter -01.644 Ŷ=b0+b1X Constant/intercept…
