Worksheet #9An analyst for a shopping district would like to determine the rent that should be charged for retailspaces depending on how close they are to parking. That is, they would like to determine the rent tocharge, using distance from parking. The analyst takes a random sample of retail spaces in similarshopping districts and measures the monthly rent ($) and distance from parking (in yards) for each retailspace.1) What are the dependent and independent variables in this analysis?y =X =Here is the scatterplot of the data:Monthyl Rent ($)180001700016000150001400013000120001100010000Rent and Distance from Parking0 25 5075 100 125 150 175 200 225 250 275 300Distance from Parking (yards)2. Do you anticipate that the regression line will have a positive or a negative slope? Why?Here is the Coefficients Table from the regression output (See the Regression Output Equationshandout-the one-page roadmap - for reference. This is the third table down):StandardError t Stat P-value249.3464 60.17 1.4E-521.5239 -7.49 5.28E-10InterceptDistance3. What is the sample intercept, bo? What is the sample slope, b₁?Coefficients15003.10-11.42Lower 95%14503.59-14.47Upper 95%15502.6-8.37 4. Write down the Estimated Regression Equation (ERE).5. What is the predicted rent for retail spaces that are 50 yards from parking? What is the predicted rentfor retail spaces that are 175 yards from parking? Interpret both of these predicted values in words.6. Graph the two points you calculated in #5 on the scatterplot above. If you can't print it out, just drawthe axes, approximate the dots, and draw your line through the two points. Use a straight edge to drawthe regression line through the two points.7. Interpret the sample slope, b₁, in words8. The lower and upper bounds of the 95% confidence interval for the population slope B₁ are reportedin the Distance row of the output in the Lower 95% and Upper 95% columns, respectively. So, the 95%confidence interval for the population slope B₁ is [-14.47, -8.37]. Interpret this interval in words.2

Given information: Coefficients Standard error t Stat P-value Lower 95% Upper 95% Intercept 15003.1 249.3464 60.17 1.40E-52 14503.59 15502.6 Distance -11.42 1.5239 -7.49 5.28E-10 -14.47 -8.371) y = Monthly Rent($) x = Distance from parking(in yards) The dependent variable is Monthly Rent($) and independent variable is Distance from parking(in yards). 2) The scatter plot shows downward trends in the data set, hence there seems to be negative relationship between Monthly Rent($) and Distance from parking(in yards). Therefore the regression line should have a negative slope.3) The sample intercept β0=15003.10 and sample slope β1=-11.42. 4) The estimated regression equation is given as y^=β0+β1·x1. β0=15003.10β1=-11.42 The estimated regression equation is y^=15003.10-11.42·x1. 5) x1 = 50 y^=15003.10-11.42·50=15003.10-571=$14432.10 The predicted rent for retail spaces that are 50 yards from parking is $14,432.10. x2 = 175 y^=15003.10-11.42·175=15003.10-1998.5=$13004.6 The predicted rent for retail spaces that are 50 yards from parking is $13,004.66) Graph two points calculated in part 5 and draw regression line through two points: 7) The sample slope β1=-11.42 means that if the Distance from parking(in yards) is increase by 1 unit then there will be decrease in the predicted value of rent by 11.42 units. 8) 95% confidence interval for the population slope β1is -14.47,-8.37. We are 95% confident that the actual slope of the regression line lies between -14.47 and -8.37. If repeated 95% confidence intervals are constructed, then the true slope of the regression line will lie in 95% of the intervals.