1. Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa.

Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa. 2 3 5 8 10 2 3 12 125 630 LA USE SALT (a) Draw a scatter diagram of the (x, y) data pairs. Do you think a straight line will be a good fit to these data? Do the y values almost seem to explode as time goes on? O No. A straight line does not fit the data well. The data does not seem to explode as x increases. O No. A straight line does not fit the data well. The data seem to explode as x increases. O Yes. A straight line does not fit the data well. The data seem to explode as x increases. O Yes. A straight line seems to fit the data well. The data seem to explode as x increases. (b) Now consider a transformation y' = log (y). We are using common logarithms of base 10. Draw a scatter diagram of the (x, y') data pairs and compare this diagram with the diagram of part (a). Which graph appears to better fit a straight line? The two diagrams are the same. The transformed data does not fit a straight line better. O The two diagrams are different. The transformed data fit a straight line better. O The two diagrams are different. The transformed data does not fit a straight line better. O The two diagrams are the same. The transformed data fit a straight line better. (c) Use a calculator with regression keys to find the linear regression equation for the data pairs (x, y'). What is the correlation coefficient? (Use 4 decimal places.) y'= r : (d) The exponential growth model is y = ap". Estimate a and B and write the exponential growth equation. (Use 4 decimal places.) a = B = V =Look at the following diagrams. Which diagrams show high linear correlation, moderate or low linear correlation, or no linear correlation? (a) (b) (c) (a ---Select--- ..... Select--- (b) no moderate (c) highThe correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient p (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of p yet. However, there is a quick way to determine if the sample evidence based on p is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if p # 0. We do this by comparing the value | | to an entry in the correlation table. The value of a in the table gives us the probability of concluding that p # 0 when, in fact, p = 0 and there is no population correlation. We have two choices for a: a = 0.05 or a = 0.01. Critical Values for Correlation Coefficient r n a = 0.05 4 = 0.01 n a = 0.05 ( = 0.01 n 0 = 0.05 C = 0.01 WN 1.0 1.00 13 0.53 0.68 23 0.4 0.53 0.95 0.99 14 0.53 0.66 0.40 0,52 un 0.8 0.96 15 0.51 0.64 0.40 0.51 6 0.81 0.92 16 0.50 0.61 0.39 0,50 0.75 0.87 17 0.48 0.61 27 0.38 0.49 8 0.71 0.83 18 0.47 0.59 0.37 0.48 9 0.6 0.80 19 0.46 0.58 29 0.37 0.47 10 0.63 0.76 20 044 0.56 30 0.36 0.46 11 0.60 0.73 21 0.43 0.55 12 0.58 0.71 22 0.42 0.54 (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of Irl large enough to conclude that weight and age of Shetland ponies are correlated? Use a = 0.05. (Round your answer for r to four decimal places. 3 6 12 19 17 60 95 140 176 186 critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. O Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.(b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of | | large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use a = 0.01. (Round your answer for r to four decimal places.) * 1004 975 992 935 972 934 40 100 65 145 65 154 critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.Reports (Vol. 62, No. 4). Consider the following data. Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer 28 45 32 47 28 23 18 25 40 13 29 34 17 52 21 14 Given the least squares line y = 42.6990 - 0.5867x: (a) Make a residual plot for the least-squares model. Be sure to plot the horizontal line at y = 0. 10 10/ 51 a 5 . . b -5 O 20 30 X 40 50 60 O 20 -X 30 40 50 60 10/ 10/ 5 C . . - 5 -5 20 X O 30 40 50 - X O 20 30 40 50 60{b} Use the residual plot to comment about the appropriateness of the least squares model for these data. 0 'he residuals do not seem to be scattered randomly around the horizontal line at [1. There do not appear to be any outliers. "he residuals seem to be scattered randomly around the horizontal line at 0. "here do appear to be outliers. O _ 0 "he residuals do not seem to be scattered randomly around the horizontal line at [1. There do appear to be outliers. O _ "he residuals seem to be scattered randomly around the horizontal line at 0. "here do not appear to be any outliers. In this problem, we use your critical values table to explore the significance of r based on different sample sizes. Critical Values for Correlation Coefficient r n \"l >