Part $2$: use the program R

The dataset $$insurance prediction$$ comes from the public domain. While the cost of treatment depends on tons of factors, including diagnostics, age, genetic factors, getting all relevant factors could be a complex task. Here, the insurance company collected information on several factors that could help them explore factors responsible for an individual$$s medical costs billed by an insurance company. The dataset has the following variables $(6$ pts$).$

CHARGES: Individual medical costs billed by health insurance

SMOKER: A binary variable $($Smoking$/$ Non$-$smoking$)$

REGION: The insured residential area in the USA $($northeast$,$ southeast, southwest, northwest$)$;

AGE: age of primary insured

SEX: female or male

BMI: body mass index

CHILDREN: Number of children covered by health insurance.

Tasks are as follows. Please provide codes for each question:

$1.$Check if there are any $"$NA$"$ and$/$or duplicate observation$/$row$.$ Ensure to tell number of duplicate observations.

$2.$Summarize the data and provide descriptive statistics.

$3.$Create two datasets $(80$:$20$ split, name train and test, respectively$).$ In the train dataset, estimate a linear regression model with $$Charges$$ as the dependent variable $($DV$),$ and rest as independent variables. Interpret the results.$$

$4.$Estimate another model by dropping the insignificant variables from the model in Q$7.$ Compare the performance $($using R$-$sq$,$ Adj, R$-$sq$,$ AIC, RMSE$)$ of the models in Q$7$ and Q$8.$

$5.$Check for the accuracy of the model in Q$8$ using QQ plot and fitted vs$.$ residual graph. Note your observations.$$

$6.$Estimate a model with log$-$transformed CHARGES as DV$,$ and age, bmi, smoker, children, smoker, region as independent variables. Compare the performance of the models from Q$7,$ Q$8,$ and Q$10.$

$7.$Are there any non$-$linear effects of Age and BMI on charges? Compute and Show