Question

C) Interpret the summary values r2 and se associated with the fitted question. Attach units to these summary statistics as appropriate.

r^2=

Se=

(Round to three decimal places as needed.)

D) What is the estimated difference in price (on average) between diamond rings with diamonds that weigh 0.18 and 0.28 carat?

The difference is _ _ _ dollars.

(Round to the near dollar as needed.)

------

Weight (carats) Price (dollars)

0.15 284

0.21 470

0.34 1,017

0.12 206

0.30 893

0.37 1,106

0.12 157

0.33 955

0.18 412

0.14 224

0.31 893

0.13 235

0.11 101

0.34 1,029

0.25 674

0.13 253

0.33 935

0.12 165

0.25 652

0.29 788

(Need help with B & C & D)

The data table found below contains the listed prices and weights of the diamonds in 20 rings offered for sale in a newspaper in a foreign city. The prices are in local dollars with the weights in carats. Complete parts (a) through (9) below. Click the icon to view the data table. OA 0 Price (dollars) Weight (carats) Price (dollars) Weight (carats) 0 0.5 ón 1200 Weight (carats) Price (dollars) Weight (carats) Price (dollars) Does there seem to be a linear trend? CA. Yes, because the scatterplot shows an approximate linear pattern OB. No, because the scatterplot does not show any obvious pattern. OC. No, because the scatterplot shows an obvious curved line. OD. Yes, because the scatterplot does not show any obvious pattern. (b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable. Complete the equation for the fitted line below. Estimated Price (local dollars) + Weight (carats) (Round to two decimal nlaces as needed

C) Interpret the summary values r2 and se associated with the fitted question. Attach units to these summary statistics as appropriate.

r2=

se=

(Round to three decimal places as needed.)

D) What is the estimated difference in price (on average) between diamond rings with diamonds that weigh 0.18 and 0.28 carat?

The difference is _ _ _ dollars.

(Round to the near dollar as needed.)

Weight (carats) Price (dollars)

0.15 284

0.21 470

0.34 1,017

0.12 206

0.30 893

0.37 1,106

0.12 157

0.33 955

0.18 412

0.14 224

0.31 893

0.13 235

0.11 101

0.34 1,029

0.25 674

0.13 253

0.33 935

0.12 165

0.25 652

0.29 788

(Need help with B & C & D)

Answer 1

	x	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)
	0.15	284	0.005776	83203.403	21.9222
	0.21	470	0.000256	10496.003	1.6392
	0.34	1017	0.012996	197624.7	50.6787
	0.12	206	0.011236	134285.6	38.8437
	0.3	893	0.005476	102752.3	23.7207
	0.37	1106	0.020736	284675.6	76.8312
	0.12	157	0.011236	172598.7	44.0377
	0.33	955	0.010816	146344.5	39.7852
	0.18	412	0.002116	25744.203	7.3807
	0.14	224	0.007396	121417.4	29.9667
	0.31	893	0.007056	102752.3	26.9262
	0.13	235	0.009216	113872.5	32.3952
	0.11	101	0.013456	222265.1	54.6882
	0.34	1029	0.012996	208437.9	52.0467
	0.25	674	0.000576	10312.403	2.4372
	0.13	253	0.009216	102048.3	30.6672
	0.33	935	0.010816	131442.5	37.7052
	0.12	165	0.011236	166015.5	43.1897
	0.25	652	0.000576	6328.2025	1.9092
	0.29	788	0.004096	46461.803	13.7952
sum	4.52	11449	0.16728	2389079	630.566
mean	0.226	572.45	sxx	syy	sxy
	slope=b1=sxy/sxx	3769.524151
	intercept=b0=ybar-(slope*xbar)	-279.4624582
	SST	SYY	2389079
	SSR	sxy^2/sxx	2376933.8
	SSE	syy-sxy^2/sxx	12145.184
	r^2	SSR/SST	0.9949164

#

b) We can form regression eqn as Price = -279.46 + 3769.52*Weight

As we can see form the eqn if we put carats Weight =0 then Price=-279.46 Hence we can say that

#The intercept is the price in dollars of a ring with a diamond weighing 0 carats.

c) r^2 = 0.9949

#se is

SSE as shown above is 12145.84

As per the definition of R^2 the interpretation is

#.The value of r2 is the fraction of the variation accounted for by the least squares regression line.

d) Difference = 3769.52*Weight₁- 3769.52*Weight₂

₌ 3769.52*0.28- 3769.52*0.18

=376.95