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(d) Interpret the meaning of the slope of the regression line.
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- For a linear regression b1 is the estimated y-intercept, and b0is the estimated slope of the regression line. True or FalseA regression analysis between cost to build a clinic (in dollars) and clinic size (in square foot) resulted in the following equation: y=75+6x. This implies that if the clinic size is 800 square feet, then the cost to build a clinic (in dollars) is?A market researcher found a correlation between advertising budgets for fliers (a, in thousands of dollars) and sales (s, in thousands of dollars) at local stores of a national pharmacy chain. Linear regression produced the equation s = 25.4a + 4.5, with r = 0.57. A local pharmacy in the chain had sales of $875 000 with a flier advertising budget of $50 000. The store manager was concerned about the accuracy of the model. a) The manager should not be concerned because the model predicts this level of sales. b) The correlation coefficient indicates a moderate correlation, so variation should be expected. c) The correlation coefficient indicates a moderate correlation, so all predictions with the model will be inaccurate. d) The manager should be concerned
- A park has kept the number of visitors since its opening in January. For the first six months of the year, the following numbers were recorded: Month Number of visitors Month Number of visitors January 133 April 640 February 183 May 1,879 March 285 June 2,550 Estimate the intercept and slope of the linear regression equation for forecasting the numbers of visitors. What are the forecasts for July through December of the year using the regression equation? The numbers of visitors to the park were 2,150 in July, and 2,660. Use Holt’s method with α=0.15 and β= 0.10 to find the one-step-ahead and two-step-ahead forecasts for September and October, respectively.You are conducting a multiple regression analysis to determine if there is a linear relationship between y, the number of applications to in-state universities and two factors: ×1, the state's unemployment rate and ×2, the average grant provided to in-state students. Ten observations are available. The analysis produced the estimated regression equation below. y = 6.5 + 2.2×1 + 4.6×2 The standard error for the intercept, unemployment rate are 9.34, and 1.23, respectively. Is the coefficient for the unemployment rate variable statistically significant at the 5% significance level? Explain. A) No, since stat = 1.39 for this coefficient, which is less than 2.365. B) No, since the p-value for this coefficient is .072, which is greater than 05 C) None of these D) No, since the p-value for this coefficient is .072, which is greater than .05Data was collected for a regression analysis where sleep quality (as a percentage) depends on the amount of caffeine consumed in a day (measured in mg). bo was found to be 92.7, b₁ was found to be -0.76, and R² was found to be 0.86. Interpret the slope of the line. O On average, each one mg increase in caffeine consumed increases a person's sleep quality by 92.7%. O On average, when x = = 0, a person has a sleep quality of -0.76%. O On average, each one mg increase in caffeine consumed decreases a person's sleep quality by 0.76%. On average, when x = 0, a person has a sleep quality of 92.7%. O We should not interpret the slope in this problem. O We should interpret the slope in this problem, but none of the above are correct.
- Using the regression formula with a slope = 5000 and intercept = 10,000, what would the predicted income be for someone who has 15 years of education? A. 60,000 B. 150,000 C. 85,000 D. 75,000(d)Assess the regression model's fitA researcher wanted to predict the sodium content (in milligrams) of beef hot dogs by looking at the calorie content. His findings from a sample of 10 beef hot dogs are summarized below. The regression equation for his data is ŷ= -299.48 + 4.35 x Calories 186 181 176 149 184 190 158 139 175 148 Sodium 495 477 425 322 482 587 370 322 479 375 Interpret the slope in terms of this problem. If appropriate, find the sodium content if the calorie content is 170. If not, why? If appropriate, find the sodium content if the calorie content is 136. If not, why?
- b. Find the equation of the regression line for the minutes the actor appeared shirtless in a film and the film's opening weekend gross. y = ___x + ____(Round to two decimal places as needed)A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents attendance (in thousands) and ŷ is the predicted number of wins. Which statement best describes the meaning of the slope of the regression line? For each increase in attendance by 1,000, the predicted number of wins increases by 4.9. For each increase in attendance by 1,000, the predicted number of wins increases by 15.2. For each increase in the number of wins by 1, the predicted attendance increases by 4,900. For each increase in the number of wins by 1, the predicted attendance increases by 15,200.A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. Which statement best describes the meaning of the slope of the regression line? For each increase in distance by 1 yard, the predicted club speed increases by 2 ft/sec. For each increase in distance by 1 yard, the predicted club speed decreases by 106 ft/sec. For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards. For each increase in club speed by 1 ft/sec, the predicted distance decreases by 106 yards.
