Simple Regression Sales Revenue Year Product Price (P) (millions of pesos) 1 1.20 0.95 1.50 0.93 2.00 0.92 4 3.50 0.90 5 4.10 0.87 5.60 0.85 Let Sales Revenue be (v) and Product Price be (x) If the Company intends plans to decrease the product price to PO.82 next year, use simple linear regression to forecast next year's sales revenue. O P43.2112 O P6.6944 O P5.4200 O P44.5327 2.

Simple Regression Sales Revenue Year Product Price (P) (millions of pesos) 1 1.20 0.95 1.50 0.93 2.00 0.92 4 3.50 0.90 5 4.10 0.87 5.60 0.85 Let Sales Revenue be (v) and Product Price be (x) If the Company intends plans to decrease the product price to PO.82 next year, use simple linear regression to forecast next year's sales revenue. O P43.2112 O P6.6944 O P5.4200 O P44.5327 2.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?
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?
Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
Cannister, Inc., specializes in the manufacture of plastic containers.The data on the monthly sales of 10-ounce shampoo bottles for the past 5 years are as follows:a. Using the multiplicative seasonal method, calculate the monthly seasonal indices.b. Develop a simple linear regression equation to forecast annual sales. For this regression, the dependent variable, Y, is the demand in each year and the independent variable, X, is the index for the year (i.e.,X = 1 for year 1, X = 2 for year 2, and so on until X = 5 for year 5). c. Forecast the annual sales for year 6 by using the regression model you developed in part (b).d. Prepare the seasonal forecast for each month by using the monthly seasonal indices calculated in part (a).
Sherry is a production manager for a small manufacturing shop and is interested in developing a predictive model to estimate the time to produce an order of a given size---- that is, that total time (in minutes) to produce a certain quantity of the product. She has collected data on the total time to produce 30 different orders of various quantities in the file Setup. A)Write out the estimated linear regression equation. ( define the variables first.) B) Interpret the intercept coefficient. C)Interpret the slope coefficient. D) Test for a significant relationship. Use α = 0.05. file Setup Quantity 105 125 135 141 149 171 190 204 206 240 255 277 299 335 371 388 392 400 421 439 439 455 458 480 486 493 506 586 589 665 Total Time 173 188 222 324 249 318 371 185 250 176 396 226 227 368 490 352 429 411 545 442 320 588 484 512 422 404 700 592 457 642
Online clothes II For the online clothing retailer dis-cussed in the previous problem, the scatterplot of Total Yearly Purchases by Income showsThe correlation between Total Yearly Purchases and Incomeis 0.722. Summary statistics for the two variables are: a) What is the linear regression equation for predictingTotal Yearly Purchase from Income? b) Do the assumptions and conditions for regression ap-pear to be met? c) What is the predicted average Total Yearly Purchasefor someone with a yearly Income of $20,000? Forsomeone with an annual Income of $80,000?d) What percent of the variability in Total YearlyPurchases is accounted for by this model?e) Do you think the regression might be a useful one forthe company? Comment.
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = β0 + β1x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: = 74.80 + 19.84 xGive a practical interpretation of the estimate of the slope of the least squares line. For a house with 0 rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the appraised value to increase $74,800. For each additional room in the house, we estimate the appraised value to increase $19,840. For each additional dollar of…
1.) Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.011 ? = y intercept of population regression line = −4 Houses in this community range in size from 1,000 to 3,000 square feet. (a) What is the mean value of gas usage (in therms) for houses with 2,100 sq. ft. of space? ____________ therms (b) What is the average change in usage (in therms) associated with a 1 sq. ft. increase in size? therms (c) What is the average change in usage (in therms) associated with a 100 sq. ft. increase in size? __________ therms (d) Should the model be used to predict mean usage for a 500 sq. ft. house? Why or why not? -No. The size of this house is too small and lies outside the range of the sample that the model is based on. -No. The…
The number of patients coming to the Healthy Start Maternity clinic has been increasing steadily over the past eight months. You are provided with some historical data as follows: Month Clinic attendance (in thousands) 1 3.4 2 3.9 3 4.5 4 5.0 5 5.8 6 5.9 7 6.5 8 6.7 Identify and give a brief explanation of the:- Dependent variable Independent variable Use simple linear regression to forecast annual demand for months 9 and 10 by using the tabular method to:- Derive the values for the intercept and slope. Derive the linear regression equation. Plot the linear regression line. iv Develop a forecast of the clinic attendance for months 9 and 10.
Let x be the size of a house (sq ft) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.014? = y intercept of population regression line = -4 (a) What is the equation of the population regression line?y = (b) What is the mean value of gas usage for houses with 2100 sq ft of space?(c) What is the average change in usage associated with a 1 square foot increase in size?(d) What is the average change in usage associated with a 100 square feet increase in size?
Using a sample of recent university graduates, you estimate a simple linear regression using initial annual salary as the dependent variable and the graduate's weighted average mark (WAM) as the explanatory variable. If the regression model has an estimated intercept of 3200 and an estimated slope coefficient of 550, what is the predicted starting salary of a student with a WAM of 75?