Update on assignment: HW3 Regression back

Question

Update I have completed 1-9 once again could someone confirm if it is right for 1-9, also could I get help on 10-12 I'm not understanding what my instructions are for 11-12.

1.) Use your judgment to draw a line on the graph that best represents the data. be sure that your line crosses the y-axis (Done already)

2.) Use your judgment to pick two points (x, y) on the line that is not on the data> (Done already) points are (20,3.90) and (70, 3.60)

3.) What quantity (in the data set) is the x-coordinate of your point associated with? (Done already, both 20 and 70 are points associated with x= Year after 1900)

4.) What quantity (in the data set) does the y-coordinate of your point measure? (Done already, both 3.90 and 3.60 are points measured with y= Time in minutes)

5.) Calculate the slope of the line joining two points. Round the slope into the fourth decimal.

(The slope of m= 3.60/70 - 3.90/20 = -.30/50 now divides the M which gives -0.006, then round it to the fourth decimal= -0.006)

6.) Your result will be a negative number, explain what the negative part means in the context of this problem (a negative number is a real number that is less than zero. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level, then negative represents below sea level.)

7.) Use the point-slope form to find the equations of the line. Then give your answer in slope-intercepted form (This is essentially a regression line) Write the y intercepted to two decimals.

(point-slope form: y-y1=m(x-x1) = y-3.90=-.30/50(x-20))

(slope-intercepted form= ymx+b = Now rewritten this y-3.90=-.30/50(x-20) to this y=-0.006x+4.02

(The y-intercepts are 4.02

8.) What is the y coordinate of the y-intercepted of the line drawn in 1, explain how you found the y-intercepted.

(Based on the first step y=time, in minutes, which had to find the first slope of m, then Point-slope form, re-written to y=mx+b, b represent y=intercepted form.)

9.) Do your results from 7 and 8 match the reason well? this is a way to check your equations. (Done both match back to 3.90 and 3.60)

10.) Use your equations from 7. to calculate the expected record time in 1974 (74 years after 1900) calculated time = (Whole number answer)

(A) Absolute error: Calculated time- Record time from data

(B) Relative error: Absolute error/(Record time from data) x 100% =

if your result is more than %5 re-check your work

11.) Use your equations from 7. to Calculate the calendar year in which the record time is 0.00 minutes.

Calcunedar year- .... (Whole number answer)

12.) Based on your above result, describe the next record time. Does that make sense explain.

Answer 1

Because you found your regression line equation:

y = -0.006 x + 4.02

y, representing the record time in minutes, and x, representing the years after 1900.

11) is asking, "So, say we set y = 0.00 (a record time of 0.00 minutes), what year after 1900 will that record time technically occur?"

Thus, 0.00 = -0.006 * x + 4.02 → 0.006 * x = 4.02 → x = 4.02/0.006 ≈ Therefore, x = 670 years after 1900

Thus, (theoretically) the record time of 0.00 minutes would happen in the year 2570.

huh, waaaaaaaay past when any of us will probably be alive (morbid but true)

12) ... the wording does not make sense on the question

"...describe the next record time"... I believe it's considering the real data set that you had to originally plot (or the next data point that lies on the regression line (?) )

If you can ask your teacher/professor for clarification there (or provide us with the data set you're working with because as it currently stands, no tutor on this site can see how the data is structured and help you to the best of their abilities)

Also, your answer to 6) is not wrong but it's not hitting the main point that I think your teacher/professor is looking for

A better record time is represented as a lower y-value on your data; if one record time is 3 minutes and another record time is 5 minutes, 3 minutes is better than 5 minutes since 3 minutes is less time than 5 minutes.

Positive slopes for a regression line describe a positive correlation

For this problem, a better record time would correlate to an earlier year (lower x means you'll get lower y)

Negative slopes for a regression line describe a negative correlation

For this problem, a better record time would correlate to a later year (higher x means you'll get lower y)

I hope this helps! If you have any questions, comments, or concerns, please feel free to message me down in the comment section of this answer!