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    Business Analytics Assingment: Neha Singh

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    Neha Singh
    The document describes analyzing data from the Ohio Department of Education on student proficiency rates across various subjects and school districts. Three regression models are developed: (1) A simple linear regression predicts math success based on a single correlated subject. This model explains 87% of variance but may not be feasible. (2) A multiple regression initially includes all subjects but eliminates non-significant predictors one by one, retaining math and science which explains 87% of variance but shows multicollinearity. (3) The models from (1) and (2) are not the same - (1) uses a single correlated variable while (2) is a full multiple regression that detects multicollinearity between math and science.

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    Business Analytics Assingment: Neha Singh

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    Neha Singh
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    The document describes analyzing data from the Ohio Department of Education on student proficiency rates across various subjects and school districts. Three regression models are developed: (1) A simple linear regression predicts math success based on a single correlated subject. This model explains 87% of variance but may not be feasible. (2) A multiple regression initially includes all subjects but eliminates non-significant predictors one by one, retaining math and science which explains 87% of variance but shows multicollinearity. (3) The models from (1) and (2) are not the same - (1) uses a single correlated variable while (2) is a full multiple regression that detects multicollinearity between math and science.

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    The document describes analyzing data from the Ohio Department of Education on student proficiency rates across various subjects and school districts. Three regression models are developed: (1) A simple linear regression predicts math success based on a single correlated subject. This model explains 87% of variance but may not be feasible. (2) A multiple regression initially includes all subjects but eliminates non-significant predictors one by one, retaining math and science which explains 87% of variance but shows multicollinearity. (3) The models from (1) and (2) are not the same - (1) uses a single correlated variable while (2) is a full multiple regression that detects multicollinearity between math and science.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    39 views7 pages

    Business Analytics Assingment: Neha Singh

    Uploaded by

    Neha Singh
    The document describes analyzing data from the Ohio Department of Education on student proficiency rates across various subjects and school districts. Three regression models are developed: (1) A simple linear regression predicts math success based on a single correlated subject. This model explains 87% of variance but may not be feasible. (2) A multiple regression initially includes all subjects but eliminates non-significant predictors one by one, retaining math and science which explains 87% of variance but shows multicollinearity. (3) The models from (1) and (2) are not the same - (1) uses a single correlated variable while (2) is a full multiple regression that detects multicollinearity between math and science.

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    of 7

    BUSINESS ANALYTICS

    ASSINGMENT

    NEHA SINGH
    PGDM Batch – 2019-21
    Roll No. & Section : 10 ‘A’

    1
    Ohio Education Performance Results Year 2000

    School District Math Writing Science Reading Citizenship All


    Indian Hill 89 95 91 98 95 83
    Wyoming 86 98 87 96 93 81
    Mason City 85 96 86 92 94 72
    Madiera 88 94 88 95 82 69
    Mariemont 74 99 88 92 89 68
    Sycamore 80 85 84 88 87 68
    Forest Hills 73 93 88 91 85 67
    Kings Local 78 92 78 86 82 64
    Lakota 73 90 81 88 85 64
    Loveland 72 85 86 93 86 61
    Southwest 73 92 73 82 78 58
    Fairf ield 71 90 77 86 83 57
    Oak Hills 75 88 79 86 77 57
    Three Rivers 66 87 77 85 84 56
    Milford 72 82 76 86 82 53
    Ross 66 84 78 85 75 52
    West Clermont 63 88 70 83 73 48
    Reading 58 88 75 80 76 46
    Princeton 59 83 63 75 76 46
    Finneytown 61 79 62 71 67 45
    Norwood 64 86 67 77 75 44
    Lockland 52 88 64 79 82 41
    Franklin City 49 85 67 79 70 40
    Winton Woods 55 82 59 77 65 40
    Northwest 51 75 61 74 62 38
    North College Hill 50 77 57 76 66 35
    Mount Healthy 40 87 53 72 62 32

    2
    Felicity Franklin 52 52 64 64 81 28
    St. Bernard 40 81 48 59 41 26
    Deer Park 40 69 52 66 43 25
    Cincinnati Public 35 63 44 59 50 23

    State Averages 60 79 68 79 72 46

    Question
    The State of Ohio Department of Education has a mandated ninth-grade proficiency test that
    covers writing, reading, mathematics, citizenship (social studies), and science. The Excel file Ohio
    Education Performance provides data on success rates (defined as the percent of students passing)
    in school districts in the greater Cincinnati metropolitan area along with state averages.

    a) Suggest the best regression model to predict math success as a function of success in the other
    subjects by examining the correlation matrix; then run the regression tool for this set of
    variables.

    Here, Science reading and citizenship are Independent variable and math is dependent variable.

    3
    Regression output summary

    R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent
    variable that's explained by an independent variable or variables in a regression model. Whereas
    correlation explains the strength of the relationship between an independent and dependent variable, R-
    squared explains to what extent the variance of one variable explains the variance of the second
    variable. So, if the R2 of a model is 0.50, then approximately half of the observed variation can be
    explained by the model's inputs.

    R Square 0.874789981
    Adjusted R Square 0.870472394

    The regression analysis shows that, by eliminating the correlated variables, the R2 value is 0.87. This
    means that there is line fit of 87%. The value of R is 0.93. Since this regression model is based on two
    variables, the model somewhat explains the data still it is not feasible. By using correlation, even though
    the model has been curated still there are other variables we need to take into account.

    4
    b) Develop a multiple regression model to predict math success as a function of success in all other
    subjects using the systematic approach described in this chapter. Is multicollinearity a problem?

    From the above model we can see that the predicted value of the “READING” variable is high as it is
    higher than 0.15 and hence it is not significant variable so we have to exclude the variable “READING”
    and re run the regression model for the rest of variables.

    5
    Now by eliminating the variable “reading” we can see that the predicted values has been reduced and
    also the model gives the better R2 value than the earlier model,still the predicted value of the remaining
    variables are higher than 0.15 and leads to the not significant variable SO we remove the variable
    “CITIZENSHIP” .

    Now we can see that by eliminating the variable “ citizenship” the value of adjusted R2 has been increased
    but still the variable “writing” has the predicted value which is higher than 0.15 hence it is also not an
    significant variable, now we will remove the variable “writing” and see how uch will it lead to the perfect
    fit model.

    6
    Now here we can see that by eliminatng the independent variables which has the predicted value more
    than 0.15 two variables left within the criteria of 0.15 hence they are the significant variable, also this
    gives us the highest value of R2 which is 0.87.
    But the question comes that multicollinearity is a problem or not.
    Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression
    model are highly linearly related. Yes multicollinearity is a problem in this model because from this we
    can see that two independent variables that is “maths and science” shows the positive relationship which
    can cause the error in fitting the model and interpreting the results.

    c) Compare the models in parts (a) and (b). Are they the same? Why or why not?

    The models (a) and (b) we can say that they are not same because in (a) part we have used the simple
    linear regression model because we have made the regression model on the basis of correlation matrix
    as we have first analyse that which independent variables has the positive strong relationship and we
    have found that maths and science has the positive relationship so on the basis of this analysis we have
    used the simple linear regression model because there is only one dependent and one independent
    variable .
    On the other hand the model in part (b) is the multiple regression model in which there is more than one
    independent variable and one dependent variable through this model we have analyse that maths and
    science have the positive relationship which shows the multicollinearity we have done this by eliminating
    the variables one by one by on the basis of the predictive value which has more than 0.15 we have
    eliminated those variables in the further steps and hence we have reached the conclusion in the end that
    maths and science shows the positive relationship.

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