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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?create a line in DESMOS with the linear regression equation: y1 - mx1 + b 2) create a second line with quadratic regression: y1 - ax1^2 + bx + c After looking at the regression in DESMOS, is the data LINEAR or QUADRATIC?To what part of the equation of the straight line < Y = MX + C > does the OLS regression coefficient correspond? - This question is based on Data Analysis A. YB. MC. XD. D
- Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?Marjorie studied the relationship between number of beers consumed (x) and blood alcohol content (y) in 34 male college students by using linear regression. The following regression equation was obtained by Marjorie from this study: y= -0.0127 + 0.0180x This equation implies that: a. each beer consumed increases blood alcohol by 1.27% b. each beer consumed increases blood alcohol by exactly 0.018 c. each beer consumed increases blood alcohol by an average of amount of 1.8% d. on average it takes 1.8 beers to increase blood alcohol content by 1%Using the table given, Which of the following is NOT necessarily true about the interpretation of the value of b in the simple linear regression equation y = a + bx for this problem? I. The monthly total costs will increase by $7.6437 for every one unit increase in the production volume. II. Since B > 0, there is a direct relationship between production volume and total costs. III. Because B > 1, there is a very strong positive linear relationship between production volume and total costs. a.) i and ii only b.) ii only c.) iii only d.) ii and iii only
- Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.10 − 0.01x and ? = 0.07. (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 12°F increase in temperature? 1°F increase hr 12°F increase hr (b) What is the expected reaction time when temperature is 190°F? When temperature is 240°F? 190°F hr 240°F hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 240°F. What is the probability that all five times are between 2.58 and 2.82 hours? (Round your answer to four decimal places.)(d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal…The police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?Q2 (a)State in algebraic notation and explain the assumption about the classical linear regression models disturbances that are referred to by the term ‘homoscedasticity’. (b)What would the consequence be for a regression model if theerrors were not homoscedastic? (c) How might you proceed if you found that (b) were actually the case? (d) What do you understand by the term ‘autocorrelation’?
- The estimated regression equation for a model involving two independent variables and 10 observations follows. y^=31.5111+0.5611x1+0.3254x2 a. Interpret b1b and b2 in this estimated regression equation (to 4 decimals ) b1____ b2____ b. Estimate y when x1=180 and x2=310 ( to 3 decimals)Using the revenue data for Yaster Inc. for the past few years, we apply linear regression to the data to find a model y= 33.2 x− 90.5, where y is Yaster's annual revenue in billions of US dollars, and x is the number of years since 2010. Use this model, together with the revenue model you found for Amazon to answer the question below. When will Yaster's revenue overtake Amazon? Note: I am asking for the year, not the number of years since 2010. This may happen between two years. Round to the nearest year.A marketing analysit is studying the relashionship between X = money spent on television advertising and Y = increase in slae. A simple linear regression model relates x and y as follows Y = 27.5 + 1.19 X What is the average change in sales associated with an additional 1 dollor spent on advertising? Group of answer choices A. For every additional 1 dollor spent on advertising, sales decreases by 1.19 dollars. B. For every additional 1 dollor spent on advertising, sales increase by 1.19 dollars. C. For every additional 1 dollor spent on advertising, sales increase by 28.69 dollars. D. For every additional 1 dollor spent on advertising, sales decreases by 28.69 dollars. E. For every additional 1 dollor spent on advertising, sales increase by 27.5 dollars.