Question

ONLY A TO C
ONLY A TO C
ONLY A TO C
ONLY A TO C

QUESTION 4 Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seem to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for striped cricket. Temperature, .x Chirps per second, 88.6 20.0 93.3 19.8 80.6 17.1 69.7 14.7 69.4 15.4 79.6 15.0 80.6 16.0 76.3 14.4 Temperature,x Chirps per second, y 71.6 16.0 84.3 18.4 75.2 15.5 82.0 17.1 83.3 16.2 82.6 17.2 83.5 17.0) Use SAS JMP or R to solve the problem and attach all your outputs!!!! (Ensure that the correlation of the two variables is included). (a) Plot a scatter diagram of the data and hence fit the regression line. (b) Briefly discuss the applicability of simple linear regression for this data set. (c) What are the estimates of bo and 4 ? Hence give the least squares regression line. (d) Interpret the slope of the regression line. (e) Test for the significance of the slope, f, at the 5% level of significance. Justify your answer by giving attention to the following detail () State the appropriate null and alternative hypothesis for this test. (ii) What test statistic is used to test these hypotheses? (iii) What is the value of the test statistic? (1) Predict the chirps per second if the temperature is 83.3°F. (g) A cricket chirps 15 times per second when the temperature is 82°F. Is this rate of chirping above or below average at this temperature? (2) (h) if it is 55°F outside. Would you recommend using the linear regression model found in part (c) to predict the number of chirps per second of a cricket? Why or why not? 3 (1) Interpret R. (2) 0) Produce a plot of residuals, do you think a linear model is appropriate for describing the relationship between temperature and chirps per second? Explain. (k) When a pair of observations is added to the data where a cricket chirps 14.5 times per second when it is 92°F outside, it gives the regression line y = 4.9565 +0.1431.x. Is this observation influential? Why? (2) (0) Find a 95% confidence interval for the chirps per second if a further experiment is performed at a temperature of 93.5" F. (10) @

Answer 1

a. ​​​​​​scatter.smooth(x,y) gives us the scatter plot and the regression line.

b. Covariance is 0.8358, very close to 1. So we can assume , chirping rate is positively correlated to temperature, and a linear regression works.

c. y=
Bix + Bo
, where y is chirping rate, and x is temperature. We get,
Bi = 0.1899, Bo = 1.3911

is the regression line and here's the plot and code-

y = 0.1899.r +1.3911