Problem 2: (10 pts) You have observations on investments (y) and profits (x) for 100 civil engineering firms. You assume that you can fit a linear regression model using OLS as follows: y=a+ẞX + ε You want to obtain estimates for a and B. a) Suppose every civil engineering firm in the sample has the same amount of profits. What, if any, problem would this create? Explain and justify your answer. b) If the distribution of the profits were not normal, can you use linear regression? Explain and justify your answer. c) If profits were presented in categories, would estimating a linear regression model be appropriate? Explain and justify your answer.

Problem 2: (10 pts) You have observations on investments (y) and profits (x) for 100 civil engineering firms. You assume that you can fit a linear regression model using OLS as follows: y=a+ẞX + ε You want to obtain estimates for a and B. a) Suppose every civil engineering firm in the sample has the same amount of profits. What, if any, problem would this create? Explain and justify your answer. b) If the distribution of the profits were not normal, can you use linear regression? Explain and justify your answer. c) If profits were presented in categories, would estimating a linear regression model be appropriate? Explain and justify your answer.

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

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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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?
Demand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00
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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
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Please help me understand this problem more in depth. A researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 2000 for each of the 52 cities randomly selected in the US. The data included information on the following variables: Deaths: The number of deaths in traffic accidents per city Income: The median income per city As part of his study, he ran the following simple linear regression model attached in photo. Question: Based on the above results, the researcher tested the hypotheses: Ho: B1=0 versus B1 not equal to 0, versus using T test. What do we know about the test statistic of the test? Based on the approximate p-value, what's the conclusion?
Problem: The following calculations have been made for prices of twelve stocks (X) on the Calcutta Stock Exchange on a certain day along with the volume of sales in thousands of shares (Y). From these calculations find the regression equation of prices on stocks, on the volume of sales of shares.
6. The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y = 1.483x - 85.072. Complete parts (a) and (b) below. Average Weekly Wages (state), x Average Weekly Wages (federal), y 754 771 800 820 837 892 924 948 995 1050 1118 1142 1198 1247 1271 1301 (a) Find the coeficient of determination and interpret the result. (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? and is represented by (3) is unexplained and is The coefficient of determination is the fraction of the variation in average weekly wages for (1) due to other factors or to sampling error. that can be explained by the variation in average weekly wages for (2) The remaining fraction of the variation, (4) (b) Find the standard error of estimate s, and interpret the result. Se = (Round to two decimal places as needed.) How can the standard error of estimate be…
Mark Price, the new productions manager for Speakers and Company, needs to find out which variable most affects the demand for their line of stereo speakers. He is uncertain whether the unit price of the product or the effects of increased marketing are the main drivers in sales and wants to use regression analysis to figure out which factor drives more demand for its particular market. Pertinent information was collected by an extensive marketing project that lasted over the past 12 years and was reduced to the data that follow: YEAR 123456789 10 11 12 UNIT SALES (THOUSANDS) 396 696 896 1,285 1,155 1,186 896 1,118 985 1,334 926 820 PRICE $/UNIT 282 219 206 210 219 209 218 206 220 206 226 236 ADVERTISING ($000) 600 829 1,118 1,413 1,214 1,285 907 1,118 708 907 708 682 a. Perform a regression analysis based on these data using Excel. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)