Strength of Regression and Prediction

Please see the attached for instructionStrength of Regression and PredictionInstructions: Complete the following questions. Enter answers and explanations in this document. Show calculations in an Excel file, using a separate worksheet (tab) for each question.1. A researcher is interested in sentencing dispositions and their relationship with the severity of a crime. She asked a sample of 10 prospective jury members to rate the seriousness of a particular crime (X) on a 1 (not very serious) to 7 (extremely serious) scale and then determine the sentence (Y) in years that sample members would recommend for that crime. The data are as follows:X Y5 127 153 34 66 101 52 25 41 35 3a. Calculate the regression slope and Y-intercept. Interpret your results.b. Predict the length of recommended sentence for a crime rated “5” on seriousness.c. Find the R-square. What does it mean?2. A researcher has gathered data from seven randomly selected correctional employees on the number of years (X) the employees have worked in a particular department and their salaries (Y) in thousands of dollars.X Y2 25.53 273 27.254 28.55 337 337 34.5a. Calculate the regression slope and Y-intercept. Interpret your results.b. What would the predicted salary be for someone in the department who has worked for 6 years?c. Find the R-square. What does it mean?3. A criminologist is interested in the effects of unemployment and policing on murder and has run the following multiple regression:Summary OutputRegression StatisticsMultiple R 0.90303R Square 0.815462Adjusted R Square 0.762737Standard Error 5.11041Observations 10 Coefficients Standard Error t Statistic P-valueIntercept –23.26309588 7.075518018 –3.28783 0.013342Unemployment rate 10.27754326 2.172859937 4.729961 0.002133Police per 100,000 –0.046737101 0.023409765 –1.99648 0.086065a. What is the Y-intercept? Interpret your results.b. Which variables are significant at the 0.05 level?c. What is the predicted homicide rate for a city with an unemployment rate of 5% and 250 police officers per 100,000 population?