Question

Goal

Your end goal is predict finishing time for all the dishes, or one of the subgroups, whichever is best.

Steps

1. Make a scatterplot of diameter vs time for all tableware. Be sure you give it a title and axis labels.
2. Check the conditions for linear regression for this scatterplot (bottom of page 385)
   1. Please use complete sentences for each condition.
3. Check the scatterplots for the subgroups – find 1 that is appropriate for linear regression.
   1. No need to include them all, just write a sentence about which one is best and how you came to that conclusion.
4. For that subgroup, include the scatterplot, correlation coefficient, and formula for the least-squares regression line
   1. Your equation should look like the one in Example 8.21, not like the y = mx + b that you enter for MyOpenMath
5. Write a sentence interpreting the slope. (Example 8.20 and page 389)
6. Write a sentence interpreting the intercept. (Example 8.20 and page 389)
7. Just overall, does it seem like predicting finishing time from diameter is going to work? Or are there too many other factors for this to be very useful? (If so, what factors?)

Data:

Bowls Casseroles Dishes Trays Plates DIAM DIAM TIME DIAM TIME DIAM TIME TIME DIAM TIME 8 34.88 10.7 47.65 10 55.53 16 54.86 12.4 23.77 10.4 17.67 14 63.13 6.5 17.46 15 44.14 16 26.09 26.52 7.4 16.41 9 58.76 5 21.04 25 109.38 11.7 31.86 5.4 12.02 10.5 43.14 11 45.12 5.5 26.53 10 6 23.21 15.4 49.48 11.1 33.71 12.3 33.89 6 20.85 28.64 12.4 48.74 9.8 44.45 19.5 64.3 11 26.25 27.76 17.8 44.95 13.5 68.63 8.8 74.48 11.1 21.87 7.5 20.21 13 86.42 11.5 34.16 14.5 23.88 14 32.62 14 33.7 12.7 31.46 5 16.66 17.84 7 12.4 32.9 7.5 20.83 22.82 12 29.48 5.5 15.61 6 13.25 12 45.78 14.2 37.11 10 23.74 13 39.71 15.2 22.55 53.18 11 21.34 8 9 20.59 8.5 30.2 LC O

Answer 1

From the given 5 categories of utensils, we obtain the scatterplots for each of their diameter and time for tableware.

They are attached below. From there we can see that subgroup 4, i.e. regression between the diameter of trays and their time for tableware can be approximated by a linear equation as all the points fall almost on or near the fitted regression line.

So, we obtain the detailed scatterplot for that subgroup which is also attached below.

The correlation coefficient for that subgroup comes out to be r = 0.936 (rounded to 3 decimal places)

The fitted linear regression equation is y4_hat = -13.987 + 4.439 x4 where y4_hat is the predicted time for the tableware given x4 is the diameter of the tray.

Interpretation of the y-intercept: If the diameter of the tray is 0 units, then we predict the time for the tableware is -13.987. (It is to be noted that in real life example this interpretation doesn't make any sense, because no tray would have diameter zero)

Interpretation of the slope: If the diameter of the tray increases by one unit, then the predicted time for the tableware will also increase by an approximate measure of 4.439 units.

(The answers are obtained using R-software. Code and output are attached below for verification).

Fle Hstory Resre Wndows RCn R Gaphics Device 2 (ACTIVE ttetancter of boyl, vi-tame tor bowis /2a/v2-2)) xl-(,10., 7.4, .4, 6, 9.9.7.5,14,7,9,12,5.5,6, 12,11.2,10, 13, 15.2, y-c(34..7.7.16.41.12.02.23.21,28.64.44.95,20.21,32.62,17.s4, plot x3, y3) 3-3)) 2-d1aete: o casseroles, y2-time for casseroles abiine (i (yt-4) ) R4 6E 63.13.576.43.24.19. 4.74 6R.63.16.42,33.7,32.9) -x5)) #x3-diameter tor dishes. y3-tise tos 4ishes x3c(10..5,5,11,11.1,9.8,8.8) 11 .s360343 y3-(55.53,17.46,21.04, 45.12,33.71.44.45,27.76) ty4-x4) Call: 1m(tormala r .25,.5.12.1. 1.5.17.8. 1.5.12.7.7.5 y-5..44.14,109.30,26.53, 33.89, 4.3,74.49,34.16,31.46,20.83)) 12 t 14 Coeftieients: (Iecercep) -13.917 4.439 plates . y5-time or plates x5-diete: ,1.86.2o.85.26.25.21.87,23.8e,1.6) ze: oec12,3) ) icx.y clet (x,v) ablinei(y-2)) Ficx,y) rlot (x5,vi alinei= (y5-x5) 4 x, v4)

RGraphics Device 2 (ACTIVE) O 90 25 20 15 10 diameter of trays 09 00 time for trays

> Cor (x4, y4) [1] 0.9360343 > lm (y4 x4) Call: lm (formula y4 x4) Coefficients: (Intercept) x4 -13.987 4.439