for a particular brand of soft drink during 10 randomly selected years. x: 103 0
ID: 3050813 • Letter: F
Question
for a particular brand of soft drink during 10 randomly selected years. x: 103 072 .071 077 .086 047 .060 .050 070 .052 y: .135 .125 .120 .086 .079 .076 .065 .059 .051 .039 (a) Construct a scatterplot for these data. Do you think the simple linear regression model (b) Calculate the equation of the estimated regression line and use it to obtain the predicted would be appropriate for describing the relationship between z and y? market share when the advertising share is .09. (c) Compute r2. How would you interpret this value? 2. (10 pts) Researchers studying pleasant touch sensations measured the firing frequency (im- pulses per second) of nerves that were stimulated by a light brushing stroke on the forearm and also recorded the subject's numerical rating of how pleasant the sensation was. The accompa- nying data was read from a graph in the paper Coding of Pleasant Touch by Unmyelinated Afferents in Humans" (Nature Neuroscience, April 12, 2009). Firing Frequency 23 24 22 25 27 28 34 33 36 34 Pleasantness Rating 0.2 1.0 1.2 1.2 1.0 2.0 2.3 2.2 2.4 2.8 (a) Estimate the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency using 95% confidence interval. Interpret the resulting interval. (b) Carry out a hypothesis test to decide if there is convincing evidence of a useful linear relationship between firing frequency and pleasantness rating 3. (10 pts) The accompanying data were read from a plot (and are a subset of the complete data set) given in the article "Cognitive Slowing in Closed-Head Injury" (Brain and Cognition [1996: 429-440). The data represent the mean response times for a group of individuals with closed-head injury (CHI) and a matched control group without head injury on 10 different tasks. Each observation was based on a different study, and used different subjects, so it is reasonable to assume that the observations are independent. Mean Response Time Control 250 CHI 303 101 StudyExplanation / Answer
(a) the linear regression y=a+bx=-2.3745+0.14*x
here regression coefficient b=0.14, so increase of 1 impulse per second in firing frequency will inceares average 0.14 unit in pleaseantness ratings
(b) here we use t-test and t=b/SE(b)=0.14/0.0257=5.45 with n-p=10-2=8 df and corresponding p-value=0.0006.
since p-value is less than alpha=0.05, so the regession coefficient is significant and we conclude that there is evidence of linear relationship
using the ms-excel following regression analysis has been performed
following data has been used for the analysis
SUMMARY OUTPUT Regression Statistics Multiple R 0.887650297 R Square 0.78792305 Adjusted R Square 0.761413431 Standard Error 0.401503414 Observations 10 ANOVA df SS MS F Significance F Regression 1 4.791360065 4.79136 29.72216 0.000607405 Residual 8 1.289639935 0.161205 Total 9 6.081 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -2.37446809 0.745414474 -3.18543 0.012892 -4.093396943 -0.655539228 X Variable 1 0.140016367 0.02568258 5.451803 0.000607 0.080792232 0.199240501Related Questions
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