City officials believe that the number of complaints to the city's heat complaint control board (for lack of heat) is directly related to the outdoor temperature. The following data have been collected: Number of complaints to Heat Control Board (24-hour period), y Outdoor Temperature, x 30°F 25°F 20°F 15ºF 10°F 5ºF 0°F 58 67 84 90 102 113 127 a. Determine the correlation coefficient between the outdoor temperature and the number of complaints. Is it reliable? b. Determine the least-squares prediction equation. c. What is the predicted number of complaints to the city's heat complaint control board when the outside temperature drops to 8°F?

Which variable pair (in part a or b or c) has a stronger association according to the comparison of the correlations and which variable pair has a stronger association according to the comparison of the p-values? Does the comparisons according to correlation coefficients and p-values agree on which variable pair indicate the same stronger association? If not, why is there such a discrepancy? Which gene pair (in part a or b or c) has a stronger association do you think according to the scatter plots? Part A: Pearson correlation of rb: 0.380875 P-value of pb: 0.0000 Significance level: α = 0.05 So, there is statistically significant association at α = 0.5 between the genes. Also, since the p-value is less than 0.05, the null hypothesis is rejected. Furthermore, the magnitude and direction are that of a positive correlation between the provided genes. Part B:  Pearson correlation of rb: 0.380875 P-value of pb: 0.0000 Significance level: α = 0.05 So, there is statistically significant…

Fifty-four wild bears were​ anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest​ sizes? When measuring an anesthetized​ bear, is it easier to measure chest size than​ weight? If​ so, does it appear that a measured chest size can be used to predict the​ weight? Use a significance level of α=0.05. Correlation Results Correlation​ coeff, r: 0.955111 Critical​ r: ±0.2680855 ​P-value (two​ tailed): 0.000         Determine the null and alternative hypotheses.   H0​: ρ less than< not equals≠ less than< greater than> equals= nothing H1​: ρ

Fifty-four wild bears were​ anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest​ sizes? When measuring an anesthetized​ bear, is it easier to measure chest size than​ weight? If​ so, does it appear that a measured chest size can be used to predict the​ weight? Use a significance level of α=0.05.                                   Correlation Results   Correlation​ coeff, r: 0.963947 Critical​ r: ±0.2680855 ​P-value (two​ tailed): 0.000 Determine the null and alternative hypotheses.   H0​: ρ is: = 0 H1​: ρ is: ≠ 0   Given all the information provided: Identify the correlation coefficient, r. r= _____ (round to three decimal places)