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1) Since 1985, average mortgage interest rates have fluctuated from a low of 4.25% to a high of 14%. Is there a relationship between the amount of money people borrow and the interest rate that's offered? Below is a scatterplot of Mortgage Loan Amount in the US (in thousands of dollars) versus Interest Rate at various times over the past 26 years. (8 pts) a) Using the scatterplot and correlation coefficient to the right, write a sentence describing the r = -0.83 relationship between Mortgage Loan Amount and 200 - 9 = 189.674 - 42.235x Interest Rate. Give your answer in terms of direction, form, and strength. 150- b) The linear regression model for this data is given to Mortgage Loan Amount ($000 the right. Interpret the slope of the model in the context of this scenario. c) Interpret the vertical intercept of the model in the 100 context of this scenario. 10 Interest Rate (X) 2) Researchers continue to look for methods to measure how fast a car was traveling before an accident. Most methods focus on the distance, d (in feet) required for an average car to completely stop while traveling at various speeds, s. Consider the table below. (14 pts) MPH (s) 20 30 40 50 60 80 Breaking Distance (d) 18 38 58 85 125 243 a) Enter the variable MPH into L1 and Breaking Distance into L2. Use the LinReg command in your graphing calculator and report the linear model and correlation coefficient. (Be sure to write the linear model as an equation and don't forget to put a "hat" over the predicted variable.) b) Use the model to predict the breaking distance for a car traveling 65 mph. c) What is the observed breaking distance for a car traveling 50 mph? What is the predicted distance for a car traveling 50 mph? d) Find the residual for a car traveling 50 mph and interpret its meaning. e) Find the residual for a car traveling 20 mph and interpret its meaning