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Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is violated in many situations. For instance, for some auditory stimuli, the Weber fraction depends systematically on the stimulus intensity. The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities x (in decibels), the Weber fraction y (in decibels) is shown. Figure 1 is a scatter plot of the data. Also given is the product of the stimulus intensity and the Weber fraction for each of the ten stimuli. (These products, written in the column labelled "xy", may aid in calculations.) Weber fraction, y (in decibels) 0 Stimulus intensity, x (in decibels) 35 -0.52 40 -0.23 45 -1.33 50 -0.86 55 -2.15 60 -2.74 65 -3.08 70 -3.11 75 -4.37 80 -4.23 Send data to calculator ✓ xy -18.2 -9.2 -59.85 -43 -118.25 -164.4 -200.2 -217.7 -327.75 -338.4 Send data to Excel Weber fraction (in decibels) X Figure 1 40 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least four decimal places. (If necessary, consult a list of formulas.) Stimulus intensity (in decibels)
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the previous year. Her data are given below, with x denoting the earnings per share from the previous year and y denoting the current stock price (both in dollars). A scatter plot of her data is shown in Figure 1. Earnings per share, x (in dollars) 59.39 21.31 15.39 42.86 42.53 38.28 49.22 57.70 52.02 33.31 29.48 29.94 26.65 42.31 18.69 36.33 Send data to calc... ✓ Send data to Excel Current stock price, y (in dollars) 2.26 0.84 0.69 1.36 0.97 1.38 1.57 2.81 2.50 1.50 0.82 1.44 1.07 1.81 0.68 1.51 Current stock price (in dollars) 0 Figure 1 10 20 30 40 50 60 Earnings per share (in dollars) The value of the sample correlation coefficient for these data is approximately 0.868. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least three decimal places. 0 (b) What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least three decimal places.