The real estate data in the excel file contains the prices Y of 414 houses. There are five explanatory variables: the age of the house (X1), distance to the nearest train station (X2), number of convenience stores (X3) and the location of the house (latitude (X4) and longitude (X5)). A real estate company collected this sample to investigate the housing prices in the area and want to use linear regression to predict housing prices. Using these data, please do each of the following:

a)Find the Pearson correlations between Y and the explanatory variables (X1, X2, X3, X4, and X5) one by one. For example Y and X1, Y and X2 and so on.

b)Plot scatter plots Y vs each X and comment your findings.

c)By using all the explanatory variables and the price of the house as a response variable, fit a regression model.

d)Is that regression model valid?

e)Which independent variables are linearly related to the housing price?

f)Make predictions by using the chosen model.

data is an attachment in the comments section