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A sociologist was hired by a large city hospital to investigate the relationship between thenumber of unauthorized days that employees are absent per year and the distance (miles)between home and work for the employees. A sample of 10 employees was chosen, andthe following data were collected.a. Develop a scatter diagram for the se data. Does a linear relationship appear reason-able? Explain.b. Develop the least squares estimated regression equation.d. Did the estimated regression equation provide a good fit? Explain.e. Use the estimated regression equation developed in part (b) to develop a 95$\%$ confi-dence interval for the expected number of days absent for employees living 5 milesfrom the company.

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Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

Piedmont College

University of St. Thomas

Boston College

Lectures

0:00

20:11

The following data resulte…

05:53

Each student in a sample o…

11:14

Number of Jobs A sociologi…

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05:15

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07:40

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07:21

Data Analysis Is the popul…

03:39

A study of the tipping hab…

05:32

To compare the commuting t…

For the following exercise…

04:20

Let $x=$ a person's &…

unopened. Nobody is this example. 55. The number or sample is 10. Significance. Living is open to the five on confidence. Interval is 95%. This is scatter plot shows the relation between the number off days absent on the vertical vaccines and distance to work on the horizontal axis. Ah, From this scatter plot, we see that there is no strong curvature present in the scatter plot. So ah, linear relationship may be reasonable to be Toby assume in order to make the regression equation Ah, literalist stayed the the necessary sound achieves signal exiles appoints is 19 Sigma X. I squared. What's the point is 1086 signal off? Uh, why it's 15 signal y squared off. The point is to 96 signal X i y i It's three 55. This sums would be needed to calculate ah, slow be which is equal to end but the blowing by it's Roy But the blight by seek Max Sigma loin uber and not the growing by excess weird but the flying By seeing my ex one square from here. Sigma X Y is this number. Sigma X is 19 from the years that boy, it's 15 Thing makes a square is 108 sits same x squared. So it's 90 90 square. So the slope from this equation will be It was negative, four point 3442 and the mean is a some old values divided by the number off. It's a valiant show extra or which is the mean is equal to sig necks. I over end, which is 90/10 just nine. And a wine bar is equal to signal Roy over and which is 50. All right, then she's fine as a Smith, a off the intercept and government is the average of why decrease by the product off basement off the slope and average Excell A is equal to why bar minus b times export, which is equal to find Sign, was negative. Four point 344 Cool times nine. Is it going toe? Ain't 0.97 78 So the general at least square equation. It's why hat is ableto alpha chase a plus beta X. So we replace Alpha with a, which is eight point all 978 and vita with B. So is equal plus ah or this is minus. This is minus being, which is 4.344 two x. So this is the equation off the medication. And let us remind the some off the square, uh, which is on its esteem in the total, um, square. She is why I minus y bar squared, is equal to 46. And this is our which isn't some off. Ah, the squares. Why Hat point us, Roy Bar Square, which is 32 0.6993 which is the vaginal from this equation, minus the meat. And this is actual value minus the me and the last. Ah, some of squared, Which is it is this is E What's the sum of square metres? It's why hats, Linus. That's what Roy Squared is equal to 13.3 or seven. The regression and leads off freedom is is one, since we have at one independent very well. So the degree of freedom was equal to toe and the errors dignities of freedom is the freedom off, and the error is equal to the simple signs decreased by the number of independent variable. She's one, so it's it's not an n minus the degree of freedom minus one, please. Then minus one minus one. So it's eight and the mean off a square, um is corresponding to the some off squares, dividing points corresponding degrees of freedom. So the end, it's our is equal toe. This s or over that they couldn't freedom. It's 3 to 6 99 3/1, just 32.6993 And the m S e some good students. Is it going toe the SS e? Well, word don't think that you need what street now. Vera, which is equal to 13.307 over over a Jay Z equals 1.6 6 to 6. The value is a probability of obtaining the value off the testes, statistics or a value more tree. And the B value here is training from the F Ah, if distribution, uh, table using the degrees of freedom Ah, the degrees of freedom you have to or the degrees of freedom of the area which is eight and the roads changed. It needs freedom. One, which is that the Chinese afraid upon the independent Very little cheeks one. So the value from the F distribution is this then no planes over. We know that is a significant living is opened or fine. Assumedly is smaller than significant living, so we reject. No, my process is so there is sufficient evidence to support that. The name that the relationship is insignificant. Question Dean, which is a proficient off determination, is the issue. R Squared is rich in between. This is our and this STD, which is equal to 32.6993 over 46 which approximately equal toe open 71 or nine, which is a sequence or 70 one point or 9%. This in the cave in at 71.9% off. Very ability between X and Y and explained by and the regression equation. So 71 of their point only is it's a high and less estimated medication equation. Provide a good fit. Eso you can say that he's that good if it were accepted are square. Ah, the confidence in turbine Mr Mind the tender they're off the estimates asunder Better in equal to ah, some of square errors over and minus two Jay Z quinto a 13.3 or seven over 10 minus two. Get your approximately is 1.2. It's mine. Evaluate the formula for the center. The Malaysians off in the goodwill and value of why, when it's b is equal to five s. O s individual is equal to is sorry is equal to it is times one over n plus XB minus X score squared. Well, we're Sigma Ex Oy minus exports. It's where so is equal to one point toe. 894 It's were off 1/10 plus five minus nine. Where over 276 So the final answer is opened. Five. Find one. We'll fight So even with the regression equation at X equal five Avoid Me is equal to 8.97 It minus 2.34 for two times experience. She's five. So the reupping in 6.37 six a. To determine the critical band using the student e distribution in the Celtic in the table and been mixed with the cream freedom equal to end minus two, which is 10 minus two. She's eight and a significant or rejection region for over two, which is one minus c over to which is your point or 25 eso that he off for over two is equal to postive or negative 2.3 old six from, um, distribution or a student in victim distribution. The boundaries off the prediction in terrible off Why Mirren become the Y hats or the white key minus thing of over two not going by its individual so is equal to or six point 3768 minus 2.3 or six times 4.515 Ah, why'd he hats lost the UN for over two times? Is in the village Would which is equal to 6.3768 plus 2.3 or six times opening 5125 This is equal to 5.4 mine ah, for nine fine and seven points by 586 eso we are 95. Confidence that the expected number off the day absent for employees living five miles from the company is between my point for ah, 95 days and 7.55 point 86 Big

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