1. The table gives the annual sales by salespersons with different years of experience in an auto dealership Years of Experience 2 5 7 8 10 12 15 18 20 Sales Volume ($1000s) 80 97 110 120 130 160 180 200 220 A. Set up a table to calculate the regression analysis B. Develop a linear regression equation for the relationships. C. Calculate the residuals for each data point and find the mean residual.
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
- A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employee. A sample of 10 employees was chosen, and the following data were collected. A. Is the estimated regression equation appropriate and adequateFind the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y150 410180 460120 320120 36070 290190 540 (a) x=160 calories (b) x=90 calories (c) x=130 calories (d) x=220 calories Y=_____x+(___)The amount of kerosene used by a typical household in a week (Q, in litres) is found to have a strong correlation with the price of kerosene (P, in $). For 6 observations, the following data was collected:Q P11.4 4.0014 3.5016 3.0018 2.5020. 2.0022 1.50(a) Create a regression relationship for this data.(b) Perform a hypothesis test to determine whether the slope coefficient obtained in part (a) above issignificant. (c) Use the regression equation in part (a) above to predict the quantity of kerosene used by a household when the price is $3.75 per litre. (d) Calculate the price elasticity of demand for kerosene at a price of $3.75 (e) Using a further calculation, discuss how well the regression equation in part (a) above fits the data.(f) Discuss whether the relationship between the price and quantity could be due to the income effect, the substitution effect, or both
- A marketing manager conducted a study to determine the relationship between money spent on advertising (X) and company sales (Y). The study consisted of 8 companies and the data is given below and is in units of $1000s (ie. 2.4 = $2400.00) d. What is the resulting residual value when advertising expenditure is $2200.00 (X = 2.2), that is the difference between the actual observed value of y and the predicted value of y when using the fitted regression equation? e. What percentage of the variation in company sales is explained by the regression equation? In other words, what is the variability in Y that is due to advertising? Does a…Write the formula for the estimated regression line and interpret the slope of the estimated regression line, the intercept of the estimated regression line- Is it meaningful?, and the estimated R2. Based on the fitted regression model, what is the predicted ATST for a child who is 7 years old? What is the correlation between AGE and ATST? Does the residual plot suggest that the fitted regression line is inappropriate for these data? Explain why or why not. Suppose that a new subject is added to the study data and that subject is 12.5 years old with an ATST of 580 minutes. If the regression model were to be refit with this additional data point, would the new slope be greater than or less than -14.041? Justify your response.Suppose a commercial developer in Vereeniging consider to purchase a group of small office buildings in an established business district. He uses multiple linear regression analysis, which was based on a sample of 35 office buildings, to estimate the value of an office building in a given area based on the following variables. Y = Assessed value of the office building (in Rand) X1= Floor space in square meters X2= Number of offices X3= Age of the office building in years Answer the questions that follow by typing only the letter of the correct option (A, B, C, D or E) in the answer spaces provided. Variablesy: Valuex1: Floor Spacex2: Officesx3: Age Model Fitting StatisticsR^2 = 0.9752Adj R^2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates Error of Beta Estimates Error of b t Statistic Prob > |t|Intcpt…
- A sample of 40 individuals collects their shoe size and the height (cm) for CSI data. The scatter plot and results from a simple linear regression are recorded: HEIGHT = 126.76238 + 4.8782178 SHOE SIZE Sample size: 40R (correlation coefficient) = 0.77918855P-value < 0.0001 (a) Does the scatterplot and results show a linear correlation between shoe size and height? (b) How can you tell? (c) Will it be appropriate to use the linear regression equation given in the output? (d) Krusty the Clown wears size 8.5 shoes. According to the linear regression equation, how tall is Krusty the Clown? (e) Sideshow Bob wears size 14 shoes. According to the linear regression equation, how tall is Sideshow Bob?The head width (in) and weight (lb) is measured for a random sample of 20 bears.The data shows that the mean head width is 6.9 inches, mean weight is 214.3 lb, and thecorrelation r = 0.879 and its p-value is less than 0.0001. The suggested linear regressionequation is WEIGHT = -212 + 61.9 WIDTH.(a) How is the best predicted weight value of a given head width found with this data found?(b) For the preceding part, why?(c) Find the best predicted weight given a bear with a head with of 6.5 inches.A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.586 Stdev width: 0.877 Mean height: 13.037 Stdev height: 1.697 Correlation coefficient: 0.7814 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.