A dataset contains 200 observations of y vs x where: S = 1.09 S, = 36.552
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- *Give the value of the correlation coefficient and interpret its meaning. Compute the least-squares regression line for predicting calories (y) from protein (x). Interpret the value of the slope. Predict the number of calories in a fast-food product containing 18 grams of protein. Round to the nearest whole number. What is the 95% confidence interval for the slope. Construct a 99% confidence interval for the slope. Test ? : ? = 0 versus ? : ? ≠ 0. Can you conclude that the amount of protein is useful in predicting the 01 11 number of calories? Use the ? = 0.05 level of significance. Is this a left-tailed test, a right-tailed test, or a two-tailed test? What is the value of the test statistic? Identify the p-value for this procedure. Do not round. Using the p-value method, should ?0 be rejected at the ? = 0.05 level of significance? Why or why not? Can we conclude that the amount of protein in fast-food products is useful in predicting the number of calories?A simple linear regression model was created based on 25 samples. The 95% confidence interval for the estimate of B, is (1.5, 4.8). What is thet-statistic for B1? Report your answer in 3 decimal places.The correlation between a response and an explanatory variable was calculated as partof a simple linear regression analysis. The corresponding 95% confidence interval forthe correlation coefficient was calculated as [-0.2, 0.2]. Without calculating anything,what can you say regarding whether the explanatory variable is a significantly usefulpredictor of the response? Explain your answer.
- A sample of 100 bears was treated like it was the whole population of Jellystone Park bears, and the mean weight was found to be 800 pounds with standard deviation 12 pounds, the mean blood pressure was 150 with standard deviation 6, and the sample correlation coefficient of weight with blood pressure was found to be .4. Based on this information, what is the regression slope for the SLR equation for predicting blood pressure using observed weight for Jellystone bears?Avalanches can be a real problem for travelers in the western United States and Canada. Slab avalanches studied in Canada had an average thickness of u = 67 cm. A sample of 31 avalanches in the U.S. gave a sample mean of = 63.0 cm. It is known that o = 10.3 cm for this type of data. Use a 0.03 level of significance to test the claim that the mean slab thickness of avalanches in the United States is different from that in Canada. Use the P-Value Approach. What are the hypotheses for this problem? А: Но и 3D 63.0 ст us На и + 63.0 ст B: Но и 63.0 ст С: Но и %3D 67 ст us HA и < 67 ст D: Ho u = 67 cm vs HA H# 67 cm B O AThe price paid for a new phone of a particular model follows a Normal distribution with mean μ=750 and standard deviation σ= 42. What proportion of these phones are purchased for more than 821 dollars? Give your answer to four decimal places. A study of 25 online jewelry retailers was done to find the statistical relationship between the price yyin dollars of a diamond ring and the weight xxin carats of the diamond. Based on this data the following least-squares regression line was found: y^=−6047.75+11975.14x What is the predicted price of diamond ring a 2.2 carat diamond using this regression line. Round your answer to two decimal places. A study of 25 online jewelry retailers was done to find the statistical relationship between the price yy in dollars of a diamond ring and the weight xx in carats of the diamond. Based on this data the following least-squares regression line was found: y^=−6047.75+11975.14x One online retailer sells a 3.00 carat diamond ring for 28,999…
- Avalanches can be a real problem for travelers in the western United States and Canada. Slab avalanches studied in Canada had an average thickness of u = 67 cm. A sample of 31 avalanches in the U.S. gave a sample mean of = 63.0 cm. It is known that o = 10.3 cm for this type of data. Use a 0.03 level of significance to test the claim that the mean slab thickness of avalanches in the United States is different from that in Canada. Use the P-Value Approach. What is the P-Value for this problem? O 0.0154 0.0150 0.0300 0.0308a sample of 60 grade 9 student age was obtained to estimate the mean age of all grade 9 students. x = 15.3 years and the population variance is 16Tire pressure (psi) and mileage (mpg) were recorded for a random sample of seven cars of thesame make and model. The extended data table (left) and fit model report (right) are based on aquadratic model What is the predicted average mileage at tire pressure x = 31?
- A car was driven 24 different times with different octane levels. Using the output from the regression, give a 82% confidence interval for the effect of octane on the car. Use 3 decimal places.Simple linear regression results:Dependent Variable: mileageIndependent Variable: octanemileage = -50.657546 + 0.9122631 octaneSample size: 24R (correlation coefficient) = 0.7165R-sq = 0.5134Estimate of error standard deviation: 1.7101924Parameter estimates: Parameter Estimate Std. Err. DF T-Stat P-Value Intercept -50.657546 -9.9406 22 5.096 <0.0001 Slope 0.9122631 0.189345 22 4.818 <0.0001Based on the scatter plot above, describe the relationship between the amount of cost damage and the distance from nearest fire station to the residential. Determine the regression line for the above regression output. Interpret the slope coefficient of distance to the nearest station affecting the amount of fire cost damage. Compute the correlation coefficient and interpret its meaning. Does the distance to the nearest fire station has significant influence on the cost damage amount? Conduct a test at 1% significance level. ] Predict the fire cost damage generated if the distance from nearest fire station is 2.5 kilometers. Is this estimate reliable? Explain. []The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in °F) for that month. The past year's usage and temperatures are in the following table by using excel: (a) Find a regression relating steam usage to temperature. (b) Test for significance of regression using a=0.05. (c) Find a 99% confidence interval for B1 Usage/ 1000 Usage/ 1000 Month Temp. Month Тemp. Jan. 21 185.79 July. 68 621.55 Feb. 24 214.47 Aug. 74 675.06 62 562.03 Sept. Oct. Mar. 32 288.03 Apr. 47 424.84 50 452.93 May 50 454.58 Nov. 41 369.95 June 59 539.03 Dec. e 30 273.98