1. From the following data and given output, determine the equation of the regression line and correlation coefficient. Test the slope of the regression model to determine whether there is a significant negative slope, use t test. Use Alpha =.05. Test also the overall model. 4 7 11 14 17 21 18 12 13 8 7 7 4
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- A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employee. A sample of 10 employees was chosen, and the following data were collected. A. Is the estimated regression equation appropriate and adequateSuppose the following data were collected from a sample of 15 houses relating selling price to square footage and the architectural style of the house. Use statistical software to find the following regression equation: PRICEi=b0+b1SQFTi+b2COLONIALi+b3RANCHi+ei . Is there enough evidence to support the claim that on average, houses that are ranch style have lower selling prices than houses that are Victorian style at the 0.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."Selling Price Square Footage Colonial (1 if house is Colonial style, 0 otherwise) Ranch (1 if house is Ranch style, 0 otherwise) Victorian (1 if house is Victorian style, 0 otherwise) 377640 1941 1 0 0 460996 3397 0 1 0 405781 2764 0 0 1 407216 2906 0 0 1 435139 3401 1 0 0 405275 2600 0 0 1 381141 2203 0 1 0 370490 2046 1 0 0 404070 2210 0 0 1 460196 3692 0 1 0 382780 2172 1 0 0 406466 2606 0 1…A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.555 Stdev width: 0.914 Mean height: 12.686 Stdev height: 1.634 Correlation coefficient: 0.8203 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
- A researcher wants to forecast the annual sales of Walmart, based on store size. To examine the relationship between the store size in square feet and its annual sales in million dollars, a sample of 14 stores was selected shown below in the image: Answer the following: i) Null hypothesis of correlation ii) Coefficient of Correlation and its interpretation iii) Interpret the sig value of ANOVA. iv) Coefficient of Determination and its interpretation v) Write down the Regression Model. vi) Interpret the value of ‘a’ vii) Interpret the value of ‘slope’Indicate whether the following statements are true or false. Explain why and show your work. c) In the regression Y=B1 + B2 X + B3 Z + u, if there is a strong linear correlation between X and Z, then it is more likely you fail to reject the null hypotheses that individual slope parameters are insignificant.Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the valye of sales ($1000) for each client sampled. Number of Contacts (X) Sales ($1000) 14 24 12 14 20 28 16 30 23 30 a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.
- A study of the amount of rainfall and the quantity of air pollution removed produced the following data shown in table below: Daily Rainfall x (0.01 cm) Particulate Removed y (μg/m3) 7 126 7.9 129.3 7.5 125.3 9.2 120.2 10.8 116.7 5.8 119.2 5.6 138.7 2.7 147.5 9.2 110.3 Compute and interpret the coefficient of determination, and coefficient of correlation for the given data. What will be the regression equation, when swapped depended and independent variableThe accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?. A researcher wants to forecast the annual sales of Walmart, based on store size. To examine the relationship between the store size in square feet and its annual sales in million dollars, a sample of 14 stores was selected shown below in the picture : Answer the following: i) Null hypothesis of correlation ii) Coefficient of Correlation and its interpretation iii) Interpret the sig value of ANOVA. iv) Coefficient of Determination and its interpretation v) Write down the Regression Model. vi) Interpret the value of ‘a’ vii) Interpret the value of ‘slope’
- Dr. Spring is a consultant for the National Youth Organization of long jumpers. His goal is to predict how farany given individual will jump (4 attempts) based only on his/her height. Fortunately he had access to height and length of jumps from last year’s competition. Initial analyses of the data were as follows: contestant height (inches) (X) Length of jumps (inches) (Y) mean: 53.100 mean: 123.650 SD: 4.667 SD: 10.535 correlation coefficient= .485, p= .030 (a) Conduct a linear regressionanalysis to predict the length of jumps for the following contestants. (do not round) Contestant number one 52inches tall, length of jumps = Contestant number two 70inches tall, length of jumps = Contestant number three 77inches tall, length of jumps =Which of the following assumptions is not necessary for unbiasedness of a slope coefficient in a multiple regression model? MLR1 MLR 4 Homoskedasticity Random samplingThe regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the data in Worksheet 2. Worksheet 2 Age of a Bus (years) Maintenance Cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 Develop a scatter diagram with the age of a bus as the independent variable. Develop the estimated regression equation that can be used to predict the maintenance cost given the age of a bus. Determine the coefficient of determination, and interpret its meaning in this problem. At the 0.05 level of significance, is there evidence of a linear relationship between the age of a bus and the annual maintenance cost.
