A paper describes a study to determine the effects of several keyboard characteristics on typing speed. One of the variables considered was the front-to-back surface angle of the keyboard. Minitab output resulting from fitting the simple linear regression model with x = surface angle (degrees) and y typing speed (words per minute) is given below. Regression Analysis: Typing Speed versus Surface Angle = The regression equation is Typing Speed Predictor Constant Surface Angle = 60.0 +0.0036 Surface Angle Coef 60.0286 SE Coef T P 0.00357 0.2466 0.03823 243.45 0.000 0.09 0.931 S = 0.511766 R-Sq = 0.3% R-Sq (adj) = 0.0% Analysis of Variance Source DF SS MS F P Regression 1 0.0023 0.0023 0.01 0.931 Residual 3 0.7857 0.2619 Error Total 4 0.788 (a) Assuming that the basic assumptions of the simple linear regression model are reasonably met, carry out a hypothesis test using α = 0.05 to decide if there is a useful linear relationship between x and y. Calculate the test statistic. (Enter your answer to two decimal places.) Calculate the test statistic. (Enter your answer to two decimal places.) t = What is the P-value for this test? (Enter your answer to three decimal places.) P-value = What can you conclude? Reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle. Do not reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle. Reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle. Do not reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle. (b) Are the values of s̟ and r² consistent with the conclusion from part (a)? Explain. e and Se show almost no linear relationship between the two variables. No, 2 Yes, r₂ and s show almost no linear relationship between the two variables.
A paper describes a study to determine the effects of several keyboard characteristics on typing speed. One of the variables considered was the front-to-back surface angle of the keyboard. Minitab output resulting from fitting the simple linear regression model with x = surface angle (degrees) and y typing speed (words per minute) is given below. Regression Analysis: Typing Speed versus Surface Angle = The regression equation is Typing Speed Predictor Constant Surface Angle = 60.0 +0.0036 Surface Angle Coef 60.0286 SE Coef T P 0.00357 0.2466 0.03823 243.45 0.000 0.09 0.931 S = 0.511766 R-Sq = 0.3% R-Sq (adj) = 0.0% Analysis of Variance Source DF SS MS F P Regression 1 0.0023 0.0023 0.01 0.931 Residual 3 0.7857 0.2619 Error Total 4 0.788 (a) Assuming that the basic assumptions of the simple linear regression model are reasonably met, carry out a hypothesis test using α = 0.05 to decide if there is a useful linear relationship between x and y. Calculate the test statistic. (Enter your answer to two decimal places.) Calculate the test statistic. (Enter your answer to two decimal places.) t = What is the P-value for this test? (Enter your answer to three decimal places.) P-value = What can you conclude? Reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle. Do not reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle. Reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle. Do not reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle. (b) Are the values of s̟ and r² consistent with the conclusion from part (a)? Explain. e and Se show almost no linear relationship between the two variables. No, 2 Yes, r₂ and s show almost no linear relationship between the two variables.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
Related questions
Question
13.2.1
Transcribed Image Text:A paper describes a study to determine the effects of several keyboard characteristics on typing speed. One of the variables considered was the front-to-back surface angle of the
keyboard. Minitab output resulting from fitting the simple linear regression model with x = surface angle (degrees) and y typing speed (words per minute) is given below.
Regression Analysis: Typing Speed versus Surface Angle
=
The regression equation is
Typing Speed
Predictor
Constant
Surface Angle
=
60.0 +0.0036 Surface Angle
Coef
60.0286
SE Coef
T
P
0.00357
0.2466
0.03823
243.45
0.000
0.09
0.931
S = 0.511766 R-Sq
=
0.3% R-Sq (adj)
= 0.0%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
1
0.0023
0.0023
0.01
0.931
Residual
3
0.7857
0.2619
Error
Total
4
0.788
(a) Assuming that the basic assumptions of the simple linear regression model are reasonably met, carry out a hypothesis test using α = 0.05 to decide if there is a useful linear
relationship between x and y. Calculate the test statistic. (Enter your answer to two decimal places.)
Calculate the test statistic. (Enter your answer to two decimal places.)
t =
What is the P-value for this test? (Enter your answer to three decimal places.)
P-value =
What can you conclude?
Reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle.
Do not reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle.
Reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle.
Do not reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle.
(b) Are the values of s̟ and r² consistent with the conclusion from part (a)? Explain.
e
and
Se
show almost no linear relationship between the two variables.
No, 2
Yes, r₂ and s show almost no linear relationship between the two variables.
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