You are trying to produce an app to replace realtors and reap their commissions (typically 5 to 6% of theproperty selling price). Your first mission is to produce a tool that helps prospective house buyers estimatethe potential selling price of their houses, and you're working on making a regression model to serve as theengine behind the tool. You'd like to make the model as simple as possible, so you are wondering how wellyou can predict the selling price of a house from just the size of the living area (ignoring garage, etc).In RStudio, run the following code to install and/or library the package "openintro".1. install.packages("openintro") # don't do this again if you already did this!2. library(openintro)3. amesDelete the install line of code if you are in an RMD file so that it doesn't install every time you knit. Thelast line of code will access the dataset of that name.The table ames' gives information about house prices in the fun college town of Ames, lowa. Use the dataset to make a model to predict the price of a house in Ames, lowa in dollars (price") from the area of livingspace of a house in square feet ("area").a. Make a scatterplot of "price" (y-axis) vs "area" (xx-axis). Which plot is the scatterplot?Graph A Graph B Graph C Graph DGraphGraphOA$4845-с5000-3000-✔BOH: B111.694HA: 111.6944000-Db. Does the relationship appear roughly linear?2900-1300No, all the points do not fall on a straight line.No, there are gaps in the graph along the x-axis.Yes, there is no obvious curvature in the graphYes, all the points fall on a straight line.c. Do the data provide strong evidence that the price of a house in Ames, lowa in dollars and the areaof living space of a house in square feet are associated! State the null and alternative hypotheses,report the p-value, and state your conclusion.1. The hypotheses are:ⒸH₂:₁0H₁:024+05d. Interpret R.Ho: 111.694H₁:111.694Ho: ₁0HA: 0II. The result of this hypothesis test is:11. The p-value for the test is (round to three decimal places if that value is 0 then enter 0.):About 49.95% of the variation in the area of living space of a house in square feet isexplained by the least squares line.Ha:B₁0HA:B₁0ⒸH₁:0HA: >0the area of living space of a house in square feet is not predictive of the price of a housein Ames, lowa in dollars.the area of living space of a house in square feet is predictive of the price of a house inAmes, lowa in dollars.About 49.95% of the variation in the price of a house in Ames, lowa in dollars isexplained by the least squares line.The total unexplained variation in the model.The total amount of variation in the model.O the amount of variation in the price of a house in Ames, lowa in dollars that is explained bythe least squares line.e. What is the equation of the regression line?Oarea - 111.694 price + 13289.634area - 13289.634 price + 111.694Oprice 13289.634 area + 111.694Oprice 111.694 area+ 13289.634The amount of variation in the area of living space of a house in square feet that is explainedby the least squares line.f. Interpret the slope in the context of the model. For each [Select an answer increase inSelect an answerSelect an answer✔Select an answerSelect an answerg. Interpret the y-intercept in the context of the model or explain why it should not be interpretedOwhen the the area of living space of a house in square feet of a house is 0 the expected valueof the price of a house in Ames, lowa in dollars is 13289.634.Owhen the the price of a house in Ames, lowa in dollars of a house is 0 the expected value ofthe area of living space of a house in square feet is 111.694.On It does not make sense to interpret the y-intercept for this model because no house in thedata had a the area of living space of a house in square feet anywhere close to 0.When the the price of a house in Ames, lowa in dollars of a house is 0 the expected value ofthe area of living space of a house in square feet is 13289.634.

> install.packages("openintro") Installing package into ‘/cloud/lib/x86_64-pc-linux-gnu-library/4.2’ (as ‘lib’ is unspecified) also installing the dependencies ‘airports’, ‘cherryblossom’, ‘usdata’ trying URL 'http://rspm/default/__linux__/focal/latest/src/contrib/airports_0.1.0.tar.gz' Content type 'application/x-gzip' length 797445 bytes (778 KB) ================================================== downloaded 778 KB trying URL 'http://rspm/default/__linux__/focal/latest/src/contrib/cherryblossom_0.1.0.tar.gz' Content type 'application/x-gzip' length 1344819 bytes (1.3 MB) ================================================== downloaded 1.3 MB trying URL 'http://rspm/default/__linux__/focal/latest/src/contrib/usdata_0.2.0.tar.gz' Content type 'application/x-gzip' length 2070047 bytes (2.0 MB) ================================================== downloaded 2.0 MB trying URL 'http://rspm/default/__linux__/focal/latest/src/contrib/openintro_2.4.0.tar.gz' Content type 'application/x-gzip' length 5159568 bytes (4.9 MB) ================================================== downloaded 4.9 MB * installing *binary* package ‘airports’ ... * DONE (airports) * installing *binary* package ‘cherryblossom’ ... * DONE (cherryblossom) * installing *binary* package ‘usdata’ ... * DONE (usdata) * installing *binary* package ‘openintro’ ... * DONE (openintro) The downloaded source packages are in ‘/tmp/RtmpYV5vkT/downloaded_packages’ > library(openintro) Loading required package: airports Loading required package: cherryblossom Loading required package: usdatax = areay = price> ames # A tibble: 2,930 × 82 Order PID area price MS.Su…¹ MS.Zo…² Lot.F…³ Lot.A…⁴ Street Alley Lot.S…⁵ Land.…⁶ Utili…⁷ <int> <int> <int> <int> <int> <fct> <int> <int> <fct> <fct> <fct> <fct> <fct> 1 1 526301100 1656 215000 20 RL 141 31770 Pave NA IR1 Lvl AllPub 2 2 526350040 896 105000 20 RH 80 11622 Pave NA Reg Lvl AllPub 3 3 526351010 1329 172000 20 RL 81 14267 Pave NA IR1 Lvl AllPub 4 4 526353030 2110 244000 20 RL 93 11160 Pave NA Reg Lvl AllPub 5 5 527105010 1629 189900 60 RL 74 13830 Pave NA IR1 Lvl AllPub 6 6 527105030 1604 195500 60 RL 78 9978 Pave NA IR1 Lvl AllPub 7 7 527127150 1338 213500 120 RL 41 4920 Pave NA Reg Lvl AllPub 8 8 527145080 1280 191500 120 RL 43 5005 Pave NA IR1 HLS AllPub 9 9 527146030 1616 236500 120 RL 39 5389 Pave NA IR1 Lvl AllPub 10 10 527162130 1804 189000 60 RL 60 7500 Pave NA Reg Lvl AllPub # … with 2,920 more rows, 69 more variables: Lot.Config <fct>, Land.Slope <fct>, # Neighborhood <fct>, Condition.1 <fct>, Condition.2 <fct>, Bldg.Type <fct>, House.Style <fct>, # Overall.Qual <int>, Overall.Cond <int>, Year.Built <int>, Year.Remod.Add <int>, # Roof.Style <fct>, Roof.Matl <fct>, Exterior.1st <fct>, Exterior.2nd <fct>, Mas.Vnr.Type <fct>, # Mas.Vnr.Area <int>, Exter.Qual <fct>, Exter.Cond <fct>, Foundation <fct>, Bsmt.Qual <fct>, # Bsmt.Cond <fct>, Bsmt.Exposure <fct>, BsmtFin.Type.1 <fct>, BsmtFin.SF.1 <int>, # BsmtFin.Type.2 <fct>, BsmtFin.SF.2 <int>, Bsmt.Unf.SF <int>, Total.Bsmt.SF <int>, … # ℹ Use `print(n = ...)` to see more rows, and `colnames()` to see all variable names > plot(ames$area,ames$price)a) The scatterplot of price (y-axis) vs area (x-axis) Option D b) The relationship does not appear linear, since many of the data points scatter and deviate away from the trend line. Hence, Option A is more appropriate > model <- lm(price~area,data=ames) > summary(model) Call: lm(formula = price ~ area, data = ames) Residuals: Min 1Q Median 3Q Max -483467 -30219 -1966 22728 334323 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 13289.634 3269.703 4.064 4.94e-05 *** area 111.694 2.066 54.061 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 56520 on 2928 degrees of freedom Multiple R-squared: 0.4995, Adjusted R-squared: 0.4994 F-statistic: 2923 on 1 and 2928 DF, p-value: < 2.2e-16 c) To test the significance of the slope of a regression line using the t-test i) The test statistic is given as: t = bSEb Null hypothesis: The slope of the regression line is equal to 0 H0:β1=0 Alternate Hypothesis: The slope of the regression line is not equal to 0 Ha:β1≠0 ii) p-value for the slope (area) is given as 0.0000000000000002 <2E-16 p-value = 0 iii) Multiple R-squared = 0.4995. This tells us that 49.95% of the variation in the response variable, that is price, can be explained by the predictor variable, area. About 49.95% of the variation in the price of a house in Ames, lowa in dollars is explained by the least squares line Option D d) Interpret R2 The amount of variation in the price of a house in Ames, lowa in dollars is explained by the least squares line Option C e) The regression line pricei^= 13289.634+111.694*areai^ Option D f) Slope = 111.694 For each square feet increase in the area, the price of a house in Ames, Lowa in dollars increases g) When the area = 0 square feet of a house is 0 the expected value of the price of a house in Ames Lowa in Dollars =13289.634 pricei^= 13289.634+111.694*areai^=13289.634+111.694*0=13289.634 Option A