Problem 5: Measuring Temperature Using Cricket Chirps Did you know that you can count cricket chirps to estimate the outdoor temperature? An amateur statistician set out to determine if this is actually possible. She listened and counted cricket chirps on a series of evenings during the late summer and recorded the temperature at the moment of counting. The dataset is called Cricket Chirps. The two explanatory variables are Chirps/15s and Time. Investigate the relationship between the explanatory variables and response variable Temp (F) by doing the following: a) Make two separate scatterplots. Each scatterplot will present one of the explanatory variables graphed with the response variable Temp (F). Copy and paste them in your solutions (use Graph Scatter Plot in StatCrunch). Title and label the graphs properly. b) Calculate the two correlation coefficients using Stat Summary Stats Correlation in StatCrunch. Each correlation will be calculated using one of the explanatory variables vs. the response variable Temp (F). Provide these two values in your document. c) Which explanatory variable has the strongest relationship with the response variable and a reason why in a complete sentence?

6 d) Interpret the scatterplot of Chirps/15s and Temp (F) using trend, strength, and shape (form) in one complete sentence. e) Using the Chirps/15s variable as the explanatory variable, run a Simple Linear Regression analysis in StatCrunch. Use Stat Regression Simple Linear. Copy and paste only the StatCrunch results output (no tables). This is the top part of the output. f) Add the fitted line plot to your document. This graph appears on page 2 of your output. g) Type the regression equation for these variables into your document. h) Interpret the slope of the regression line (in context of this data set). i) Is it meaningful to interpret the y-intercept? Why or why not? j) State r 2 (i.e., the coefficient of determination) and explain what this value means in context of the data set. k) Use the regression equation from part (g) to predict a random nights temperature when 55 chirps were counted in 15 seconds. State your predicted value in a sentence that is in context of the data. Note, you can do this calculation by hand or using StatCrunch. l) Is your prediction in part (k) an example of extrapolation? Why or why not?