1. Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.

1. Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?
.The worker has noticed that the more time he spends at work (x), the less money he is likely to make (y) in conducting transactions for his firm. Which of the regression equations MOST suggests such a possibility?
I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that the relationship between X1 and Y is significant the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant. the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2 the estimated mean of Y is 2 when X1 equals zero.
If the equation of the regression line that relates hours per week spent in the tutor lab, x, to GPA, y, is y=2.1+0.28, then the best presdiction for the GPA of students who never go into the lab would be 2.1 True Or False
Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?
Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual starting salary of an employee with a doctorate degree? (Someone with no work experience). $ What is the predicted bi-annual starting salary of an employee with a bachelor’s degree? (Someone with no work experience). $
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…
If the points (x1, y1), (x2, y2),..., (xn, yn) lie on a straight line, what can you say about the regression line associated with these points?
Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE. Y X1 X2 1 40 25 2 45 20 1 38 30 3 50 30 2 48 28 3 55 30 3 53 34 4 55 36 4 58 32 3 40 34 5 55 38 3 48 28 3 45 30 2 55 36 4 60 34 5 60 38 5 60 42 5 65 38 4 50 34 3 58 38 Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.