According to "Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana,"† the size of a female salamander's snout is correlated with the number of eggs in her clutch. The following data are consistent with summary quantities reported in the article. Partial Minitab output is also included. Snout-Vent Length Clutch Size 32 45 53 215 53 160 53 170 54 190 57 200 57 270 58 175 58 245 59 215 63 170 63 240 64 245 67 280 The regression equation is Y = -133 + 5.92x Predictor Coef Stdev T P Constant -133.02 64.30 2.07 0.0608 x 5.919 1.127 5.25 0.0002 s = 33.90 R-sq = 69.7% R-sq(adj) = 67.2% Additional summary statistics are given below. n = 14 x = 56.5 y = 201.4 Σx2 = 45,597 Σy2 = 613,550 Σxy = 164,690 You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What is the equation of the regression line for predicting clutch size based on snout-vent length? (Let x = snout vent length and y = clutch size. Round your intercept to two decimal places and your slope to three decimal places.) ŷ = _______ (b) What is the value of the estimated standard deviation of b? (Round your answer to three decimal places.) __________ (c) Is there sufficient evidence to conclude that the slope of the population line is positive? No. Since the estimated slope is positive and since the P-value is small we do not have convincing evidence that the slope of the population regression line is positive. Yes. Since the estimated slope is positive and since the P-value is small we have convincing evidence that the slope of the population regression line is positive. Yes. Since the estimated slope is positive and since the P-value is large we have convincing evidence that the slope of the population regression line is positive. No. Since the estimated slope is positive and since the P-value is large we do not have convincing evidence that the slope of the population regression line is positive. (d) Predict the clutch size for a salamander with a snout-vent length of 50 using a 95% interval. (Round your answers to three decimal places. If it is not appropriate to find a prediction interval, enter NA in both blanks.) ( ___ , ___ ) (e) Predict the clutch size for a salamander with a snout-vent length of 115 using a 90% interval. (Round your answers to three decimal places. Round your answers to three decimal places. If it is not appropriate to find a prediction interval, enter NA in both blanks.) (___ , ___)

According to "Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana,"† the size of a female salamander's snout is correlated with the number of eggs in her clutch. The following data are consistent with summary quantities reported in the article. Partial Minitab output is also included. Snout-Vent Length Clutch Size 32 45 53 215 53 160 53 170 54 190 57 200 57 270 58 175 58 245 59 215 63 170 63 240 64 245 67 280 The regression equation is Y = -133 + 5.92x Predictor Coef Stdev T P Constant -133.02 64.30 2.07 0.0608 x 5.919 1.127 5.25 0.0002 s = 33.90 R-sq = 69.7% R-sq(adj) = 67.2% Additional summary statistics are given below. n = 14 x = 56.5 y = 201.4 Σx2 = 45,597 Σy2 = 613,550 Σxy = 164,690 You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What is the equation of the regression line for predicting clutch size based on snout-vent length? (Let x = snout vent length and y = clutch size. Round your intercept to two decimal places and your slope to three decimal places.) ŷ = _ (b) What is the value of the estimated standard deviation of b? (Round your answer to three decimal places.) __ (c) Is there sufficient evidence to conclude that the slope of the population line is positive? No. Since the estimated slope is positive and since the P-value is small we do not have convincing evidence that the slope of the population regression line is positive. Yes. Since the estimated slope is positive and since the P-value is small we have convincing evidence that the slope of the population regression line is positive. Yes. Since the estimated slope is positive and since the P-value is large we have convincing evidence that the slope of the population regression line is positive. No. Since the estimated slope is positive and since the P-value is large we do not have convincing evidence that the slope of the population regression line is positive. (d) Predict the clutch size for a salamander with a snout-vent length of 50 using a 95% interval. (Round your answers to three decimal places. If it is not appropriate to find a prediction interval, enter NA in both blanks.) ( _ , _ ) (e) Predict the clutch size for a salamander with a snout-vent length of 115 using a 90% interval. (Round your answers to three decimal places. Round your answers to three decimal places. If it is not appropriate to find a prediction interval, enter NA in both blanks.) (_ , ___)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 31PPS

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Related questions

Question

Snout-Vent Length	Clutch Size
32	45
53	215
53	160
53	170
54	190
57	200
57	270
58	175
58	245
59	215
63	170
63	240
64	245
67	280

The regression equation is
Y = -133 + 5.92x
Predictor	Coef	Stdev	T	P
Constant	-133.02	64.30	2.07	0.0608
x	5.919	1.127	5.25	0.0002
s = 33.90 R-sq = 69.7% R-sq(adj) = 67.2%

Additional summary statistics are given below.

n	=	14	x	=	56.5	y	=	201.4
Σx²	=	45,597	Σy²	=	613,550	Σxy	=	164,690

You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question.

(a)

What is the equation of the regression line for predicting clutch size based on snout-vent length? (Let x = snout vent length and y = clutch size. Round your intercept to two decimal places and your slope to three decimal places.)

ŷ = _______

(b)

What is the value of the estimated standard deviation of b? (Round your answer to three decimal places.)

__________

(c)

Is there sufficient evidence to conclude that the slope of the population line is positive?

No. Since the estimated slope is positive and since the P-value is small we do not have convincing evidence that the slope of the population regression line is positive.

Yes. Since the estimated slope is positive and since the P-value is small we have convincing evidence that the slope of the population regression line is positive.

Yes. Since the estimated slope is positive and since the P-value is large we have convincing evidence that the slope of the population regression line is positive.

No. Since the estimated slope is positive and since the P-value is large we do not have convincing evidence that the slope of the population regression line is positive.

(d)

Predict the clutch size for a salamander with a snout-vent length of 50 using a 95% interval. (Round your answers to three decimal places. If it is not appropriate to find a prediction interval, enter NA in both blanks.)

( ___ , ___ )

(e)

Predict the clutch size for a salamander with a snout-vent length of 115 using a 90% interval. (Round your answers to three decimal places. Round your answers to three decimal places. If it is not appropriate to find a prediction interval, enter NA in both blanks.)

(___ , ___)

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